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- Vyjayanthi Chari, Andrew Pressley
- 1997

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)

- Vyjayanthi Chari, Andrew Pressley
- 1994

We prove a highest weight classification of the finite-dimensional irreducible representations of a quantum affine algebra, in the spirit of Cartan's classification of the finite-dimensional irreducible representations of complex simple Lie algebras in terms of dominant integral weights. We also survey what is currently known about the structure of these… (More)

- 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)

- Vyjayanthi Chari, Andrew Pressley
- 1996

- Vyjayanthi Chari, Andrew Pressley
- 2001

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, Andrew Pressley
- 1996

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)

- Vyjayanthi Chari, Andrew Pressley
- 1996

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)

- Jonathan Beck, Vyjayanthi Chari, Andrew Pressley
- 1999

The canonical basis for finite type quantized universal enveloping algebras was introduced in [L3]. The principal technique is the explicit construction (via the braid group action) of a lattice L over Z[q −1 ]. This allows the algebraic characterization of the canonical basis as a certain bar-invariant basis of L. Here we present a similar algebraic… (More)