Vyjayanthi Chari

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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)
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)
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)
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)