Crystals for Demazure Modules of Classical Affine Lie Algebras

1997/07/11 by Atsuo Kuniba, A. Kuniba, K. C. Misra +12
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #q-alg

paper · pdf · doi:10.48550/arxiv.q-alg/9707014

Latex, 28 pages

arxiv created 1997/07/11 · openalex publication_date 1997/07/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study, in the path realization, crystals for Demazure modules of affine Lie algebras of types A⁽¹⁾_n,B⁽¹⁾_n,C⁽¹⁾_n,D⁽¹⁾_n, A⁽²⁾_2n-1,A⁽²⁾_2n, and D⁽²⁾_n+1. We find a special sequence of affine Weyl group elements for the selected perfect crystal, and show if the highest weight is l\La₀, the Demazure crystal has a remarkably simple structure.

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