Characters and Blocks for Finite-Dimensional Representations of Quantum Affine Algebras

2004/06/08 by Vyjayanthi Chari, Chari, Vyjayanthi, Adriano Moura +1 · 2 citations
Mathematics · Physics and Astronomy · #17B10 #20G42 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Quantum many-body systems #Representation Theory (math.RT) #math.QA #math.RT #msc:17B10 #msc:20G42

paper · pdf · doi:10.48550/arxiv.math/0406151

Revised version. To appear in IMRN

openalex publication_date 2004/06/08 · arxiv created 2004/12/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of the ell-weight lattice and the ell-root lattice adapted to the study of finite-dimensional representations of quantum affine algebras. We then study the ell-weights of the fundamental representations and show that they are invariant under the action of the associated braid group, in the case when the underlying simple Lie algebra is of classical type. As an application of this result we are able to give explicit formulas for their q-characters. An example is worked out in detail in Section 5. Finally, we describe the blocks in the category and prove that they are parametrized by the quotient of the ell-weight lattice by the ell-root lattice.

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• Extremal monomials of q-characters
• Quiver moduli and quantum loop algebras

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