Braid Group Actions and Tensor Products

2001/06/28 by Vyjayanthi Chari, Chari, Vyjayanthi · 5 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.math/0106241

This paper is an expanded version of math.qa/0012116. The results are stronger, and the conditions implied by the braid group action are made explicit

arxiv created 2001/06/28 · arxiv updated 2009/11/30

Abstract

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 corresponding R--matrix has a zero.

Cited by

• Extremal monomials of q-characters
• Elliptic Central Characters and Blocks of Finite Dimensional Representations of Quantum Affine Algebras
• Quantum cluster algebras and representations of shifted quantum affine algebras
• t-analogs of q-characters of Kirillov-Reshetikhin modules of quantm affine algebras
• Parabolic quantum affine algebras

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