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- VYJAYANTHI CHARI
- 2001

The irreducible finite-dimensional representations of quantum affine algebras These representations decompose as a direct sum of ir-reducible representations of the quantized eneveloping algebra U q (g) associated to the underlying finite-dimensional simple Lie algebra g. But, except for a few special cases, little is known about the isotypical components… (More)

LetˆU q be the quantized universal enveloping algebra of affine sl 2 , and letˆU res q be the C[q, q −1 ]-subalgebra ofˆU q generated by the q-divided powers of the Chevalley generators. LetˆU res ǫ be the Hopf algebra obtained fromˆU res q by specialising q to an odd root of unity ǫ. We classify the finite-dimensional irreducible representations ofˆU res q… (More)

The study of the irreducible finite–dimensional representations of quantum affine algebras has been the subject of a number of papers, [AK], [CP3], [CP5], [FR], [FM], [GV], [KS] to name a few. However, the structure of these representations is still unknown except in certain special cases. In this paper, we approach the problem by studying the classical (q… (More)

One of the most beautiful results from the classical period of the representation theory of Lie groups is the correspondence, due to Frobenius and Schur, between the representations of symmetric groups and those of general or special linear groups. If V 0 is the natural irreducible (n + 1)–dimensional representation of SL n+1 (C I), the symmetric group S ℓ… (More)

We study connections between the ring of symmetric functions and the characters of irreducible finite-dimensional representations of quantum affine algebras. We study two families of representations of the symplectic and orthogonal Lie algebras. One is defined via combinatorial properties and is easy to calculate; the other is closely related to the q = 1… (More)

- VYJAYANTHI CHARI
- 2008

We define an action of the braid group of a simple Lie algebra on the space of imaginary roots in the corresponding quantum affine algebra. We then use this action to determine an explicit condition for a tensor product of arbitrary irreducible finite–dimensional representations is cyclic. This allows us to determine the set of points at which the… (More)

- VYJAYANTHI CHARI
- 2008

The notion of a Weyl module, previously defined for the untwisted affine algebras, is extended here to the twisted affine algebras. We describe an identification of the Weyl modules for the twisted affine algebras with suitably chosen Weyl modules for the untwisted affine algebras. This identification allows us to use known results in the untwisted case to… (More)

Introduction In this paper we study the category C of finite–dimensional representations of affine Lie algebras. The irreducible objects of this category were classified and described explicitly in [2],[4]. It was known however that C was not semisimple. In such a case a natural problem is to describe the blocks of the category. The blocks of an abelian… (More)