#### Filter Results:

- Full text PDF available (27)

#### Publication Year

1996

2016

- This year (0)
- Last 5 years (2)
- Last 10 years (11)

#### Publication Type

#### Co-author

#### Journals and Conferences

#### Key Phrases

Learn More

Quantum affine algebras are one of the most important classes of quantum groups. Their finite-dimensional representations lead to solutions of the quantum Yang– Baxter equation which are trigonometric functions of the spectral parameter (see [7], Sect. 12.5 B) and are thus related to various types of integrable models in statistical mechanics and field… (More)

- VYJAYANTHI CHARI
- 2001

The irreducible finite-dimensional representations of quantum affine algebras Uq(ĝ) have been studied from various viewpoints, [AK], [CP1], [CP3], [C], [CP4], [FR], [FM], [KR], [KS]. These representations decompose as a direct sum of irreducible representations of the quantized eneveloping algebra Uq(g) associated to the underlying finite-dimensional simple… (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 V0 is the natural irreducible (n+ 1)–dimensional representation of SLn+1(CI), the symmetric group Sl acts… (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)

- VYJAYANTHI CHARI
- 1997

Let Uq(ĝ) be the quantized universal enveloping algebra of the affine Lie algebra ĝ associated to a finite-dimensional complex simple Lie algebra g, and let U res q (ĝ) be the C[q, q−1]-subalgebra of Uq(ĝ) generated by the q-divided powers of the Chevalley generators. Let U res (ĝ) be the Hopf algebra obtained from U res q (ĝ) by specialising q to a… (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)

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 category are… (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)

Let t be an arbitrary symmetrizable Kac-Moody Lie algebra and Uq(t) the corresponding quantized enveloping algebra of t defined over C(q). If μ is a dominant integral weight of t then one can associate to it in a natural way an irreducible integrable Uq(t)-module L(μ). These modules have many nice properties and are well understood, [K], [L1]. More… (More)

In this paper we define and study a family of Z+–graded modules for the polynomial valued current algebra g[t] and the twisted current algebra g[t] associated to a finite–dimensional classical simple Lie algebra g and a non–trivial diagram automorphism of g. The modules which we denote as KR(mωi) and KR (mωi) respectively are indexed by pairs (i,m), where i… (More)