Bethe Ansatz for the Universal Weight Function (2008)
Frappat, L., Khoroshkin, S., Pakuliak, S., Ragoucy, E.
We consider universal off-shell Bethe vectors given in terms of Drinfeld realization of the algebra $U_q(\widehat{gl}_N)$ [arXiv:math/0610517,arXiv:0711.2819]. We investigate ordering properties of...
Thermodynamical limit of general gl(N) spin chains II: Excited states and energies (2007)
Crampe, N., Frappat, L., Ragoucy, E.
We consider the thermodynamical limit of a gl(N) spin chain with arbitrary representation at each site of the chain. We consider excitations (with holes and new strings) above the vacuum and compute...
Super-Hubbard models and applications (2007)
Drummond, J. M., Feverati, G., Frappat, L., Ragoucy, E.
We construct XX- and Hubbard- like models based on unitary superalgebras gl(N|M) generalising Shastry's and Maassarani's approach of the algebraic case. We introduce the R-matrix of the gl(N|M) XX...
Thermodynamical limit of general gl(N) spin chains: vacuum state and densities (2007)
Crampe, N., Frappat, L., Ragoucy, E.
We study the vacuum state of spin chains where each site carry an arbitrary representation. We prove that the string hypothesis, usually used to solve the Bethe ansatz equations, is valid for...
Sugawara and vertex operator constructions for deformed Virasoro algebras (2006)
Arnaudon, D., Avan, J., Frappat, L., Ragoucy, E., Shiraishi, J.
From the defining exchange relations of the A_{q,p}(gl_{N}) elliptic quantum algebra, we construct subalgebras which can be characterized as q-deformed W_N algebras. The consistency conditions...
Sugawara and vertex operator constructions for deformed Virasoro algebras (2006)
Arnaudon, D., Avan, J., Frappat, L., Ragoucy, E., Shiraishi, J.
From the defining exchange relations of the A_{q,p}(gl_{N}) elliptic quantum algebra, we construct subalgebras which can be characterized as q-deformed W_N algebras. The consistency conditions...
Sugawara and vertex operator constructions for deformed Virasoro algebras (2006)
Arnaudon, D., Avan, J., Frappat, L., Ragoucy, E., Shiraishi, J.
From the defining exchange relations of the A_{q,p}(gl_{N}) elliptic quantum algebra, we construct subalgebras which can be characterized as q-deformed W_N algebras. The consistency conditions...
Sugawara and vertex operator constructions for deformed Virasoro algebras (2006)
Arnaudon, D., Avan, J., Frappat, L., Ragoucy, E., Shiraishi, J.
From the defining exchange relations of the A_{q,p}(gl_{N}) elliptic quantum algebra, we construct subalgebras which can be characterized as q-deformed W_N algebras. The consistency conditions...
Arnaudon, D., Crampe, N., Doikou, A., Frappat, L., Ragoucy, E.
We consider the N-site U_{q}(gl(N)) integrable spin chain with periodic and open diagonal soliton-preserving boundary conditions. By employing analytical Bethe ansatz techniques we are able to...
Arnaudon, D., Avan, J., Crampe', N., Doikou, A., Frappat, L., Ragoucy, E.
We present a classification of diagonal, antidiagonal and mixed reflection matrices related to Yangian and super-Yangian R matrices associated to the infinite series so(m), sp(n) and osp(m|n). We...
Super Yangian Y(osp(1|2)) and the Universal R-matrix of its Quantum Double (2005)
Arnaudon, D., Crampe', N., Frappat, L., Ragoucy, E.
We present the Drinfel\'d realisation of the super Yangian Y(osp(1|2)), including the explicit expression for the coproduct. We show in particular that it is necessary to introduce supplementary...
Yangian and quantum universal solutions of Gervais--Neveu--Felder equations (2005)
Arnaudon, D., Avan, J., Frappat, L., Ragoucy, E.
We construct universal Drinfel\'d twists defining deformations of Hopf algebra structures based upon simple Lie algebras and contragredient simple Lie superalgebras. In particular, we obtain deformed...
On the Quasi-Hopf structure of deformed double Yangians (2005)
Arnaudon, D., Avan, J., Frappat, L., Ragoucy, E., Rossi, M.
We construct universal twists connecting the centrally extended double Yangian DY(sl(2))_c with deformed double Yangians DY_r(sl(2))_c, thereby establishing the quasi-Hopf structures of the latter.
Analytical Bethe ansatz in gl(N) spin chains (2005)
Arnaudon, D., Crampe, N., Doikou, A., Frappat, L., Ragoucy, Eric
We present a global treatment of the analytical Bethe ansatz for gl(N) spin chains admitting on each site an arbitrary representation. The method applies for closed and open spin chains, and also to...
Analytical Bethe ansatz in gl(N) spin chains (2005)
Arnaudon, D., Crampe, N., Doikou, A., Frappat, L., Ragoucy, Eric
We present a global treatment of the analytical Bethe ansatz for gl(N) spin chains admitting on each site an arbitrary representation. The method applies for closed and open spin chains, and also to...
Analytical Bethe ansatz in gl(N) spin chains (2005)
Arnaudon, D., Crampe, N., Doikou, A., Frappat, L., Ragoucy, Eric
We present a global treatment of the analytical Bethe ansatz for gl(N) spin chains admitting on each site an arbitrary representation. The method applies for closed and open spin chains, and also to...
Analytical Bethe ansatz in gl(N) spin chains (2005)
Arnaudon, D., Crampe, N., Doikou, A., Frappat, L., Ragoucy, Eric
We present a global treatment of the analytical Bethe ansatz for gl(N) spin chains admitting on each site an arbitrary representation. The method applies for closed and open spin chains, and also to...
Analytical Bethe ansatz in gl(N) spin chains (2005)
Arnaudon, D., Crampe, N., Doikou, A., Frappat, L., Ragoucy, Eric
We present a global treatment of the analytical Bethe ansatz for gl(N) spin chains admitting on each site an arbitrary representation. The method applies for closed and open spin chains, and also to...
Analytical Bethe Ansatz for open spin chains with soliton non preserving boundary conditions (2005)
Arnaudon, D., Crampe, N., Doikou, A., Frappat, L., Ragoucy, E.
We present an ``algebraic treatment'' of the analytical Bethe ansatz for open spin chains with soliton non preserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and...
Analytical Bethe Ansatz for open spin chains with soliton non preserving boundary conditions (2005)
Arnaudon, D., Crampe, N., Doikou, A., Frappat, L., Ragoucy, E.
We present an ``algebraic treatment'' of the analytical Bethe ansatz for open spin chains with soliton non preserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and...
Analytical Bethe Ansatz for open spin chains with soliton non preserving boundary conditions (2005)
Arnaudon, D., Crampe, N., Doikou, A., Frappat, L., Ragoucy, E.
We present an ``algebraic treatment'' of the analytical Bethe ansatz for open spin chains with soliton non preserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and...
Analytical Bethe Ansatz for open spin chains with soliton non preserving boundary conditions (2005)
Arnaudon, D., Crampe, N., Doikou, A., Frappat, L., Ragoucy, E.
We present an ``algebraic treatment'' of the analytical Bethe ansatz for open spin chains with soliton non preserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and...
On sl(N) and sl(M|N) integrable open spin chains (2004)
Arnaudon, D., Avan, J., Crampe', N., Doikou, A., Frappat, L., Ragoucy, E.
We study open spin chains based on rational sl(N) and sl(M|N) R-matrices. We classify the solutions of the reflection equations, for both the soliton-preserving and soliton-non-preserving cases. We...
Hyperbolic Kac-Moody superalgebras (2004)
We present a classification of the hyperbolic Kac-Moody (HKM) superalgebras. The HKM superalgebras of rank larger or equal than 3 are finite in number (213) and limited in rank (6). The Dynkin-Kac...
Sum rules for free energy and frequency distribution of DNA dinucleotides (2003)
The large discrepancy between the values of the free energy for DNA dinucleotides (or dimers) measured by different teams has raised a yet unsettled debate. Here the free energy is fitted by a three...
Introduction s, briefly, remind how the DNA ruI0 the synthesis of proteins, whichconstituP the most abutfl0 t organicsunicfl100 in living matter systems. The DNA macromolecu1 is made of two linear...
Universality and Shannon entropy of codon usage (2003)
Frappat, L, Minichini, C, Sciarrino, A, Sorba, Paul
The distribution functions of the codon usage probabilities, computed over all the available GenBank data, for 40 eukaryotic biological species and 5 chloroplasts, do not follow a Zipf law, but are...
Universality and Shannon entropy of codon usage (2003)
Frappat, L., Sciarrino, A., Sorba, P.
The distribution functions of the codon usage probabilities, computed over all the available GenBank data, for 40 eukaryotic biological species and 5 chloroplasts, do not follow a Zipf law, but are...
Correlation matrix for quartet codon usage (2003)
Frappat, L, Sciarrino, A, Sorba, Paul
It has been argued that the sum of usage probabilities for codons, belonging to quartets, that have as third nucleotide C or A, is independent of the biological species for vertebrates. The...
Correlation matrix for quartet codon usage (2003)
Frappat, L., Sciarrino, A., Sorba, P.
It has been argued that the sum of usage probabilities for codons, belonging to quartets, that have as third nucleotide C or A, is independent of the biological species for vertebrates. The...
Arnaudon, D., Avan, J., Crampe', N., Doikou, A., Frappat, L., Ragoucy, E.
We present a classification of diagonal, antidiagonal and mixed reflection matrices related to Yangian and super-Yangian R matrices associated to the infinite series so(m), sp(n) and osp(m|n). We...
Arnaudon, D., Avan, J., Crampe', N., Doikou, A., Frappat, L., Ragoucy, E.
We present a classification of diagonal, antidiagonal and mixed reflection matrices related to Yangian and super-Yangian R matrices associated to the infinite series so(m), sp(n) and osp(m|n). We...
Arnaudon, D., Avan, J., Crampe', N., Doikou, A., Frappat, L., Ragoucy, E.
We present a classification of diagonal, antidiagonal and mixed reflection matrices related to Yangian and super-Yangian R matrices associated to the infinite series so(m), sp(n) and osp(m|n). We...
Super Yangian Y(osp(1|2)) and the Universal R-matrix of its Quantum Double (2002)
Arnaudon, D., Crampe', N., Frappat, L., Ragoucy, E.
We present the Drinfel'd realisation of the super Yangian Y(osp(1|2)), including the explicit expression for the coproduct. We show in particular that it is necessary to introduce supplementary Serre...
Sum rules of codon usage probabilities (2002)
Frappat, L., Sciarrino, A., Sorba, P.
In the crystal basis model of the genetic code, it is deduced that the sum of usage probabilities of the codons with C and A in the third position for the quartets and/or sextets is independent of...
Quantum elliptic algebras and double Yangians (2002)
Quantum universal enveloping algebras, quantum elliptic algebras and double (deformed) Yangians provide fundamental algebraic structures relevant for many integrable systems. They are described in...
Super Yangian Y(osp(1|2)) and the Universal R-matrix of its Quantum Double (2002)
Arnaudon, D., Crampe', N., Frappat, L., Ragoucy, E.
We present the Drinfel\'d realisation of the super Yangian Y(osp(1|2)), including the explicit expression for the coproduct. We show in particular that it is necessary to introduce supplementary...
Super Yangian Y(osp(1|2)) and the Universal R-matrix of its Quantum Double (2002)
Arnaudon, D., Crampe', N., Frappat, L., Ragoucy, E.
We present the Drinfel\'d realisation of the super Yangian Y(osp(1|2)), including the explicit expression for the coproduct. We show in particular that it is necessary to introduce supplementary...
R-matrix presentation for (super)-Yangians Y(g) (2001)
Arnaudon, D., Avan, J., Crampe, N., Frappat, L., Ragoucy, E.
We give a unified RTT presentation of (super)-Yangians Y(g) for so(n), sp(2n) and osp(m|2n).
Yangian and quantum universal solutions of Gervais--Neveu--Felder equations (2001)
Arnaudon, D., Avan, J., Frappat, L., Ragoucy, E.
We construct universal Drinfel'd twists defining deformations of Hopf algebra structures based upon simple Lie algebras and contragredient simple Lie superalgebras. In particular, we obtain deformed...
Yangian and quantum universal solutions of Gervais--Neveu--Felder equations (2001)
Arnaudon, D., Avan, J., Frappat, L., Ragoucy, E.
We construct universal Drinfel\'d twists defining deformations of Hopf algebra structures based upon simple Lie algebras and contragredient simple Lie superalgebras. In particular, we obtain deformed...
Yangian and quantum universal solutions of Gervais--Neveu--Felder equations (2001)
Arnaudon, D., Avan, J., Frappat, L., Ragoucy, E.
We construct universal Drinfel\'d twists defining deformations of Hopf algebra structures based upon simple Lie algebras and contragredient simple Lie superalgebras. In particular, we obtain deformed...
A minimum principle in mRNA editing ? (2000)
Frappat, L., Sciarrino, A., Sorba, P.
mRNA editing of sequences of many species is analyzed. The nature of the inserted nucleotides and the position of the insertion sites, once fixed the edited peptide chain, are explained by...
Theoretical prevision of physical chemical properties of amino acids from genetic code (2000)
Frappat, L., Sciarrino, A., Sorba, P.
Using the crystal basis model of the genetic code, a set of relations between the physical-chemical properties of the amino acids are derived and compared with the experimental data. A prevision for...
Crystalizing the genetic code (2000)
Frappat, L., Sciarrino, A., Sorba, P.
New developments are presented in the framework of the model introduced by the authors in refs. [1,2] and in which nucleotides as well as codons are classified in crystal bases of the quantum group...
On the Quasi-Hopf structure of deformed double Yangians (2000)
Arnaudon, D., Avan, J., Frappat, L., Ragoucy, E., Rossi, M.
We construct universal twists connecting the centrally extended double Yangian DY(sl(2))_c with deformed double Yangians DY_r(sl(2))_c, thereby establishing the quasi-Hopf structures of the latter.
On the Quasi-Hopf structure of deformed double Yangians (2000)
Arnaudon, D., Avan, J., Frappat, L., Ragoucy, E., Rossi, M.
We construct universal twists connecting the centrally extended double Yangian DY(sl(2))_c with deformed double Yangians DY_r(sl(2))_c, thereby establishing the quasi-Hopf structures of the latter.
On the Quasi-Hopf structure of deformed double Yangians (2000)
Arnaudon, D., Avan, J., Frappat, L., Ragoucy, E., Rossi, M.
We construct universal twists connecting the centrally extended double Yangian DY(sl(2))_c with deformed double Yangians DY_r(sl(2))_c, thereby establishing the quasi-Hopf structures of the latter.
Cladistics of Double Yangians and Elliptic Algebras (1999)
Arnaudon, D., Avan, J., Frappat, L., Ragoucy, E., Rossi, M.
A self-contained description of algebraic structures, obtained by combinations of various limit procedures applied to vertex and face sl(2) elliptic quantum affine algebras, is given. New double...
Deformed Double Yangian Structures (1999)
Arnaudon, D., Avan, J., Frappat, L., Rossi, M.
Scaling limits when q tends to 1 of the elliptic vertex algebras A_qp(sl(N)) are defined for any N, extending the previously known case of N=2. They realise deformed, centrally extended double...
Symmetry and Codon Usage Correlations in the Genetic Code (1998)
Frappat, L., Sciarrino, A., Sorba, P.
The ratios of the codon usage in the quartets and sextets for the vertebrate series exhibit a correlated behaviour which fits naturally in the framework of the crystal basis model of the genetic...
q-deformed W-algebras and elliptic algebras (1998)
Avan, J., Frappat, L., Rossi, M., Sorba, P.
The elliptic algebra A_{q,p}(sl(N)_{c}) at the critical level c=-N has an extended center containing trace-like operators t(z). Families of Poisson structures, defining q-deformations of the W_N...
Universal construction of W_{p,q} algebras (1998)
Avan, J., Frappat, L., Rossi, M., Sorba, P.
We present a direct construction of abstract generators for q-deformed W_N algebras. This procedure hinges upon a twisted trace formula for the elliptic algebra A_{q,p}(sl(N)_c) generalizing the...
Central extensions of classical and quantum q-Viraroso algebras (1998)
Avan, J., Frappat, L., Rossi, M., Sorba, P.
We investigate the central extensions of the q-deformed (classical and quantum) Virasoro algebras constructed from the elliptic quantum algebra A_{q,p}[sl(N)_c]. After establishing the expressions of...
A crystal base for the genetic code (1998)
Frappat, L., Sciarrino, A., Sorba, P.
The quantum enveloping algebra U_q(sl(2) \oplus sl(2)) in the limit q \to 0 is proposed as a symmetry algebra for the genetic code. In this approach the triplets of nucleotids or codons in the DNA...
Deformed W_N algebras from elliptic sl(N) algebras (1998)
Avan, J., Frappat, L., Rossi, M., Sorba, P.
We extend to the sl(N) case the results that we previously obtained on the construction of W_{q,p} algebras from the elliptic algebra A_{q,p}(\hat{sl}(2)_c). The elliptic algebra...
From quantum to elliptic algebras (1997)
Avan, J., Frappat, L., Rossi, M., Sorba, P.
It is shown that the elliptic algebra ${\cal A}_{q,p}(\hat{sl}(2)_c)$ at the critical level c=-2 has a multidimensional center containing some trace-like operators t(z). A family of Poisson...
Avan, J., Frappat, L., Rossi, M., Sorba, P.
We construct operators t(z) in the elliptic algebra introduced by Foda et al. ${\cal A}_{q,p}({\hat sl}(2)_c)$. They close an exchange algebra when p^m=q^{c+2} for m integer. In addition they commute...
Classification of the quantum deformation of the superalgebra $GL(1|1)$ (1997)
Frappat, L., Hussin, V., Rideau, G.
We present a classification of the possible quantum deformations of the supergroup $GL(1|1)$ and its Lie superalgebra $gl(1|1)$. In each case, the (super)commutation relations and the Hopf structures...
Poisson structures on the center of the elliptic algebra A_{p,q}(sl(2)_c) (1997)
Avan, J., Frappat, L., Rossi, M., Sorba, P.
It is shown that the elliptic algebra A_{p,q}(sl(2)_c) has a non trivial center at the critical level $c=-2$, generalizing the result of Reshetikhin and Semenov-Tian-Shansky for trigonometric...
Anyonic Realization of the Quantum Affine Lie Superalgebra U_q(A(M,N)^{(1)}) (1996)
Frappat, L., Sciarrino, A., Sciuto, S., Sorba, P.
We give a realization of the quantum affine Lie superalgebras U_q(A(M,N))^(1) in terms of anyons defined on a one or two-dimensional lattice, the deformation parameter q being related to the...
Dictionary on Lie Superalgebras (1996)
Frappat, L., Sciarrino, A., Sorba, P.
The main definitions and properties of Lie superalgebras are proposed a la facon de a short dictionary, the different items following the alphabetical order. The main topics deal with the structure...
Anyonic Realization of the Quantum Affine Lie Algebras (1996)
Frappat, L., Sciarrino, A., Sciuto, S., Sorba, P.
We give a realization of the quantum affine Lie algebras $\uqa$ and $\uqc$ in terms of anyons defined on a one-dimensional chain (or on a two-dimensional lattice), the deformation parameter $q$ being...
Arnaudon, D., Bauer, M., Frappat, L.
We define on the universal enveloping superalgebra of osp(1|2n) a nonstandard adjoint action, endowing it with a module structure. This allows, in particular, to construct a bosonic operator which...
Anyonic Realization of the Quantum Affine Lie Algebra U_q(A_N) (1995)
Frappat, L., Sciarrino, A., Sciuto, S., Sorba, P.
We give a realization of quantum affine Lie algebra $U_q(\hat A_{N-1})$ in terms of anyons defined on a two-dimensional lattice, the deformation parameter $q$ being related to the statistical...
Classical and Quantum sl(1|2) Superalgebras, Casimir Operators and Quantum Chain Hamiltonians (1995)
Arnaudon, D., Chryssomalakos, C., Frappat, L.
We examine the two parameter deformed superalgebra $U_{qs}(sl(1|2))$ and use the results in the construction of quantum chain Hamiltonians. This study is done both in the framework of the Serre...
Delduc, F., Frappat, L., Ragoucy, E., Sorba, P.
We perform an Hamiltonian reduction on a classical \cw(\cg, \ch) algebra, and prove that we get another \cw(\cg, \ch$'$) algebra, with $\ch\subset\ch'$. In the case $\cg=S\ell(n)$, the existence of a...
General properties of classical W algebras (1993)
Delduc, F., Frappat, L., Ragoucy, E., Sorba, P.
After some definitions, we review in the first part of this talk the construction and classification of classical $W$ (super)algebras symmetries of Toda theories. The second part deals with more...
Rational $ W $ algebras from composite operators (1993)
Delduc, F., Frappat, L., Sorba, P., Toppan, F., Ragoucy, E.
Factoring out the spin $1$ subalgebra of a $ W $ algebra leads to a new $ W $ structure which can be seen either as a rational finitely generated $ W $ algebra or as a polynomial non-linear $...
Frappat, L., Ragoucy, E., Sorba, P.
In the same way the folding of the Dynkin diagram of A_{2n} (resp. A_{2n-1}) produces the B_n (resp. C_n) Dynkin diagram, the symmetry algebra W of a Toda model based on B_n (resp. C_n) can be seen...
(SUPER) W Algebras from Non Abelian (SUPER) Toda Theories (1992)
Frappat, L., Ragoucy, E., Sorba, P.
A classification of (super) $W$ algebras arising from non Abelian Toda and super Toda theories is presented. This classification is based on the $Sl(2)$ or $OSp(1|2)$ sub(super)algebras of the simple...
W Algebras and Superalgebras from Constrained WZW Models: A Group Theoretical Classification (1992)
Frappat, L., Ragoucy, E., Sorba, P.
We present a classification of $W$ algebras and superalgebras arising in Abelian as well as non Abelian Toda theories. Each model, obtained from a constrained WZW action, is related with an $Sl(2)$...