Lakshmibai-Seshadri paths for hyperbolic Kac-Moody algebras of rank 2

2017/02/08 by Yu, Dongxiao
#FOS: Mathematics #Quantum Algebra (math.QA)

paper · doi:10.48550/arxiv.1702.02320

Abstract

Let \mathfrakg be a hyperbolic Kac-Moody algebra of rank 2, and set λ: = Λ₁ - Λ₂, where Λ₁, Λ₂ are the fundamental weights for \mathfrakg; note that λ is neither dominant nor antidominant. Let \mathbbB(λ) be the crystal of all Lakshmibai-Seshadri paths of shape λ. We prove that (the crystal graph of) \mathbbB(λ) is connected. Furthermore, we give an explicit description of Lakshmibai-Seshadri paths of shape λ.

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