We study the higher spin analogs of the six-vertex model on the basis of its symmetry under the quantum affine algebra [Formula: see text]. Using the method developed recently for the XXZ spin chain, we formulate the space of states, transfer matrix, vacuum, creation/ annihilation operators of particles, and local operators, purely in the language of representation theory. We find that, regardless of the level of the representation involved, the particles have spin 1/2, and that the n-particle space has an RSOS type structure rather than a simple tensor product of the one-particle space. This agrees with the picture proposed earlier by Reshetikhin.

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International audienc

Abstract. For a commutative algebra A over a commutative ring k satisfying certain conditions, we construct the universal central extension of g k ⊗ k A , regarded as a Lie superalgebra over k , where g k denotes a basic classical Lie superalgebra over k . To consider basic classical Lie superalgebras over an ring k , we also show the existence of their Chevalley basis. Our results contain not only the descriptions of the untwisted affine Lie superalgebras but also those of the toroidal Lie superalgebras. Mathematics Subject Classification (2000). 17B05, 17B55, 19D55.

We discuss a construction of highest weight modules for the recently defined elliptic algebra A q,p ( sl 2 ), and make several conjectures concerning them. The modules are generated by the action of the components of the operator L on the highest weight vectors. We introduce the vertex operators Φ and Ψ * through their commutation relations with the L-operator. We present ordering rules for the Land Φ-operators and find an upper bound for the number of linearly independent vectors generated by them, which agrees with the known characters of sl 2 -modules. IntroductionIn our previous paper [1] we defined the elliptic quantum affine algebra A q,p (ĝ) with g = gl 2 or sl 2 . The present paper is an attempt toward understanding the correct elliptic analogues of the highest weight modules and vertex operators. Our aim here is to present conjectures concerning their existence and expected properties, along with some experimental computations to support them. *

On the basis of 'RT T = T T R' formalism, we introduce the quantum double of the Yangian Y (g) for g = gl N , sl N with a central extension. The Gauss decomposition of T-matrices gives us the so-called Drinfel'd generators. Using these generators, we present some examples of both finite and infinite dimensional representations that are quite natural deformations of the corresponding affine counterpart.

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