Abdesselam, B., Chakrabarti, A.
For a class of multiparameter statistical models based on $N^2\times N^2$ braid matrices the eigenvalues of the transfer matrix ${\bf T}^{(r)}$ are obtained explicitly for all $(r,N)$. Our formalism...
A new eight vertex model and higher dimensional, multiparameter generalizations (2008)
Abdesselam, B., Chakrabarti, A.
We study statistical models, specifically transfer matrices corresponding to a multiparameter hierarchy of braid matrices of $(2n)^2\times(2n)^2$ dimensions with $2n^2$ free parameters...
Higher Dimensional Multiparameter Unitary and Nonunitary Braid Matrices: Even Dimensions (2007)
Abdesselam, B., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
A class of $(2n)^2\times(2n)^2$ multiparameter braid matrices are presented for all $n$ $(n\geq 1)$. Apart from the spectral parameter $\theta$, they depend on $2n^2$ free parameters...
Abdesselam, B., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.
We construct $(2n)^2\times (2n)^2$ unitary braid matrices $\hat{R}$ for $n\geq 2$ generalizing the class known for $n=1$. A set of $(2n)\times (2n)$ matrices $(I,J,K,L)$ are defined. $\hat{R}$ is...
Addendum to "On Super-Jordanian ${\cal U}_{\sf h}(sl(N|1))$ Algebra (2007)
Abdesselam, B., Chakrabarti, A., Chakrabarti, R., Yanallah, A., Zahaf, M. B.
We give a complete proof of the result (2.10) presented in our paper published in J. Phys. A: Math. Gen. 39 (2006) 8307.
Abdesselam, B., Chakrabarti, A.
Statistical models corresponding to a new class of braid matrices ($\hat{o}_N; N\geq 3$) presented in a previous paper are studied. Indices labeling states spanning the $N^r$ dimensional base space...
Abdesselam, B., Chakrabarti, A.
Our starting point is a class of braid matrices, presented in a previous paper, constructed on a basis of a nested sequence of projectors. Statistical models associated to such $N^2\times N^2$...
On super-Jordanian ${\cal U}_{\sf h}(sl(N|1))$ algebra (2005)
Abdesselam, B., Chakrabarti, A., Chakrabarti, R., Yanallah, A., Zahaf, M. B.
A nonlinear realisation of the nonstandard (super-Jordanian) deformed ${\cal U}_{\sf h}(sl(N|1))$ algebra is given for arbitrary $N$.
Jordanian Quantum Algebra ${\\cal U}_{\\sf h}(sl(N))$ via Contraction Method and Mapping (2005)
Abdesselam, B., Chakrabarti, A., Chakrabarti, R.
Using the contraction procedure introduced by us in Ref. \\cite{ACC2}, we construct, in the first part of the present letter, the Jordanian quantum Hopf algebra ${\\cal U}_{\\sf h}(sl(3))$ which has...
Jordanian Quantum (Super)Algebras $U_{h}(g)$ via Contraction Method and Mapping:Review (2004)
Abdesselam, B., Chakrabarti, R., Yanallah, A., Zahaf, M. B.
Recently, a class of transformations of $R_q$-matrices was introduced such that the $q \to 1$ limit gives explicit nonstandard $R_h$-matrices. The transformation matrix is singular as $q \to 1$. For...
On Nonstandard Quantizations of osp(2|1) Superalgebra via Contraction and Mapping (2003)
Abdesselam, B., Chakrabarti, R., Hazzab, A., Yanallah, A.
We develop a generic reprersentation-independent contraction procedure for obtaining, for instance, $R_{\sf h}$ and $L$ operators of arbitrary dimensions for the quantized ${\cal U}_{\sf...
Non-factorisable metrics and Gauss--Bonnet terms in higher dimensions (2002)
Abdesselam, B., Chakrabarti, A., Rizos, J., Tchrakian, D. H.
An iterative construction of higher order Einstein tensors for a maximally Gauss-Bonnet extended gravitational Lagrangian was introduced in a previous paper. Here the formalism is extended to...
Brane World Cosmology with Gauss-Bonnet Interaction (2001)
We study a Randall-Sundrum model modified by a Gauss-Bonnet interaction term. We consider, in particular, a Friedmann-Robertson-Walker metric on the brane and analyse the resulting cosmological...
Jordanian Quantum Algebra ${\cal U}_{\sf h}(sl(N))$ via Contraction Method and Mapping (2001)
Abdesselam, B., Chakrabarti, A., Chakrabarti, R.
Using the contraction procedure introduced by us in Ref. \cite{ACC2}, we construct, in the first part of the present letter, the Jordanian quantum Hopf algebra ${\cal U}_{\sf h}(sl(3))$ which has a...
Jordanian Quantum Algebra ${\\cal U}_{\\sf h}(sl(N))$ via Contraction Method and Mapping (2001)
Abdesselam, B., Chakrabarti, A., Chakrabarti, R.
Using the contraction procedure introduced by us in Ref. \\cite{ACC2}, we construct, in the first part of the present letter, the Jordanian quantum Hopf algebra ${\\cal U}_{\\sf h}(sl(3))$ which has...
Jordanian Quantum Algebra ${\\cal U}_{\\sf h}(sl(N))$ via Contraction Method and Mapping (2001)
Abdesselam, B., Chakrabarti, A., Chakrabarti, R.
Using the contraction procedure introduced by us in Ref. \\cite{ACC2}, we construct, in the first part of the present letter, the Jordanian quantum Hopf algebra ${\\cal U}_{\\sf h}(sl(3))$ which has...
Maps and twists relating $U(sl(2))$ and the nonstandard $U_{h}(sl(2))$: unified construction (1998)
Abdesselam, B., Chakrabarti, A., Chakrabarti, R., Segar, J.
A general construction is given for a class of invertible maps between the classical $U(sl(2))$ and the Jordanian $U_{h}(sl(2))$ algebras. Different maps are directly useful in different contexts....
General Construction of Nonstandard $R_h$-matrices as Contraction Limits of $R_{q}$-matrices (1997)
Abdesselam, B., Chakrabarti, A., Chakrabarti, R.
A class of transformations of $R_q$-matrices is introduced such that the $q\to 1$ limit gives explicit nonstandard $R_{h}$-matrices. The transformation matrix is singular itself at $q\to 1$ limit....
Combined (q,h)-Deformation as a Nonlinear Map on $U_q(sl(2))$ (1996)
Abdesselam, B., Chakrabarti, A., Chakrabarti, R.
The generators $(J_{\pm}, J_0)$ of the algebra $U_q(sl(2))$ is our starting point. An invertible nonlinear map involving, apart from q, a second arbitrary complex parameter h, defines a triplet...
On ${\cal U}_h(sl(2))$, ${\cal U}_h(e(3))$ and their Representations (1996)
Abdesselam, B., Chakrabarti, A., Chakrabarti, R.
By solving a set of recursion relations for the matrix elements of the ${\cal U}_h(sl(2))$ generators, the finite dimensional highest weight representations of the algebra were obtained as factor...
Abdesselam, B., Chakrabarti, A., Chakrabarti, R.
The generators of the Jordanian quantum algebra ${\cal U}_h(sl(2))$ are expressed as nonlinear invertible functions of the classical $sl(2)$ generators. This permits immediate explicit construction...
Centre and Representations of U_q(sl(2|1)) at Roots of Unity (1996)
Abdesselam, B., Arnaudon, D., Bauer, M.
Quantum groups at roots of unity have the property that their centre is enlarged. Polynomial equations relate the standard deformed Casimir operators and the new central elements. These relations are...
On Nonlinear Angular Momentum Theories, Their Representations and Associated Hopf Structures (1996)
Abdesselam, B., Beckers, J., Chakrabarti, A., Debergh, N.
Nonlinear $sl(2)$ algebras subtending generalized angular momentum theories are studied in terms of undeformed generators and bases. We construct their unitary irreducible representations in such a...
Non--Minimal $q$--Deformations and Orthogonal Symmetries: $U_q$(SO(5)) Example (1995)
Abdesselam, B., Arnaudon, D., Chakrabarti, A.
Non--minimal $q$-deformations are defined. Their role in the explicit construction of the matrix elements of the generators of ${\cal U}_{q}(SO(5))$ on suitably parametrized bases are exhibited. The...
On the Fundumental Invariant of the Hecke Algebra $H_{n}(q)$ (1995)
Katriel, J., Abdesselam, B., Chakrabarti, A.
The fundumental invariant of the Hecke algebra $H_{n}(q)$ is the $q$-deformed class-sum of transpositions of the symmetric group $S_{n}$. Irreducible representations of $H_{n}(q)$, for generic $q$,...
On a Deformation of $sl(2)$ with Paragrassmannian Variables (1995)
Abdesselam, B., Beckers, J., Chakrabarti, A., Debergh, N.
We propose a new structure ${\cal U}^{r}_{\displaystyle{q}}(sl(2)) $. This is realized by multiplying $\delta$ ($q=e^{\delta}$, $\delta\in \CC$) by $\theta$, where $\theta$ is a real nilpotent...
Representations of U_q(sl(N)) at Roots of Unity (1995)
Abdesselam, B., Arnaudon, D., Chakrabarti, A.
The Gelfand--Zetlin basis for representations of $U_q(sl(N))$ is improved to fit better the case when $q$ is a root of unity. The usual $q$-deformed representations, as well as the nilpotent,...
Katriel, J., Abdesselam, B., Chakrabarti, A.
The traces of the Murphy operators of the Hecke algebra $H_n(q)$, and of products of sets of Murphy operators with non-consecutive indices, can be evaluated by a straightforward recursive procedure....
Katriel, J., Abdesselam, B., Chakrabarti, A.
The irreducible representations (irreps) of the Hecke algebra $H_n(q)$ are shown to be completely characterized by the fundamental invariant of this algebra, $C_n$. This fundamental invariant is...
Representations of $SO(5)_{q}$ and Non-Minimal $q$-Deformation (1994)
Abdesselam, B., Arnaudon, D., Chakrabarti, A.
Representations of $SO(5)_{q}$ can be constructed on bases such that either the Chevalley triplet $(e_{1},\;f_{1},\;h_{1})$ or $(e_{2},\;f_{2},\;h_{2})$ has the standard $SU(2)_{q}$ matrix elements....