Connectedness of Lakshmibai-Seshadri path crystals for hyperbolic Kac-Moody algebras of rank 2

2020/01/04 by Ryuta Hiasa, Hiasa, Ryuta
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.2001.01066

22 pages, 3 figures; to appear in Comm. Algebra

arxiv created 2020/08/29 · arxiv updated 2020/09/01

Abstract

Let \mathfrakg be a hyperbolic Kac-Moody algebra of rank 2. We give a necessary and sufficient condition for the crystal graph of the Lakshmibai-Seshadri path crystal \mathbbB(λ) to be connected for an arbitrary integral weight λ.

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