Polyhedral Realizations of Crystal Bases for Integrable Highest Weight Modules

1998/06/16 by Toshiki Nakashima, Nakashima, Toshiki
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.CO #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.math/9806085

LaTeX, 27 pages, some reference is added

arxiv created 1998/07/01 · arxiv updated 2009/11/30

Abstract

We give a general way of representing the crystal (base) corresponding to the intgrable highest weight modules of quantum Kac-Moody algebras, which is called polyhedral realizations. This is applied to describe explicitly the crystal bases of integrable highest weight modules for arbitrary rank 2 Kac-Moody algebra cases, the classical A_n-case and the affine A⁽¹⁾_n-1-case.

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