Scientific Commons: D. Arnaudon

Irreducible representations of the quantum analogue of SU(2) (2007)

We give the complete set of irreducible representations of U(SU(2))_q when q is a m-th root of unity. In particular we show that their dimensions are less or equal to m. Some of them are not highest...

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...

Exotic Bialgebra S03: Representations, Baxterisation and Applications (2006)

Arnaudon, D., Chakrabarti, A., Dobrev, V. K., Mihov, S. G.

The exotic bialgebra S03, defined by a solution of the Yang-Baxter equation, which is not a deformation of the trivial, is considered. Its FRT dual algebra $s03_F$ is studied. The Baxterisation of...

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...

Spectrum and Bethe ansatz equations for the U_ {q}(gl(N)) closed and open spin chains in any representation (2005)

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...

On the R-matrix realization of Yangians and their representations (2005)

Arnaudon, D., Molev, A., Ragoucy, E.

We study the Yangians Y(a) associated with the simple Lie algebras a of type B, C or D. The algebra Y(a) can be regarded as a quotient of the extended Yangian X(a) whose defining relations are...

Multi-leg integrable ladder models (2005)

Arnaudon, D., Sedrakyan, A., Sedrakyan, T.

We construct integrable spin chains with inhomogeneous periodic disposition of the anisotropy parameter. The periodicity holds for both auxiliary (space) and quantum (time) directions. The...

Integrable XYZ Model with Staggered Anisotropy Parameter (2005)

Arnaudon, D., Karakhanyan, D., Mirumyan, M., Sedrakyan, A., Sorba, P.

We apply to the XYZ model the technique of construction of integrable models with staggered parameters, presented recently for the XXZ case. The solution of modified Yang-Baxter equations is found...

Generalization of the U_q(gl(N)) algebra and staggered models (2005)

Arnaudon, D., Sedrakyan, A., Sedrakyan, T., Sorba, P.

We develop a technique of construction of integrable models with a Z_2 grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy...

Integrable Chain Model with Additional Staggered Model Parameter (2005)

Arnaudon, D., Poghossian, R., Sedrakyan, A., Sorba, P.

The generalization of the Yang-Baxter equations (YBE) in the presence of Z_2 grading along both chain and time directions is presented. The XXZ model with staggered disposition along a chain of both,...

Classification of reflection matrices related to (super) Yangians and application to open spin chain models (2005)

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