Finite Dimensional Representations of Quantum Affine Algebras

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dc.creatorKleber, Michael
dc.date1998-09-16
dc.date.accessioned2026-07-07T05:26:02Z
dc.date.available2026-07-07T05:26:02Z
dc.descriptionWe investigate the characters of some finite-dimensional representations of the quantum affine algebras $U_q(\hat{g})$ using the action of the copy of $U_q(g)$ embedded in it. First, we present an efficient algorithm for computing the Kirillov-Reshetikhin conjectured formula for these characters when $g$ is simply-laced. This replaces the original formulation, in terms of "rigged configurations", with one based on polygonal paths in the Weyl chamber. It also gives a new algorithm for decomposing a tensor product of any number of representations of $sl(n)$ corresponding to rectangular Young diagrams, in a way symmetric in all the factors. This section is an expanded version of q-alg/9611032 . Second, we study a generalization of certain remarkable quadratic relations that hold among characters of $sl(n)$ (the "discrete Hirota relations") whose solutions seem to be characters of quantum affine algebras. We use show that these relations have a unique solution over characters of $U_q(g)$.
dc.descriptionLaTeX, 55 pages, requires Paul Taylor's macro package diagrams.tex. Ph.D. dissertation at University of Californial Berkeley
dc.identifierhttps://arxiv.org/abs/math/9809087
dc.identifierhttp://arxiv.org/abs/math/9809087
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77406
dc.subjectQuantum Algebra
dc.subjectCombinatorics
dc.subjectRepresentation Theory
dc.titleFinite Dimensional Representations of Quantum Affine Algebras
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