Polyhedral realization of the crystal bases for extremal weight modules over quantized hyperbolic Kac-Moody algebras of rank 2

DOI10.1016/J.JALGEBRA.2023.01.019arXiv2112.02493MaRDI QIDQ6384841

Ryuta Hiasa

Publication date: 5 December 2021

Abstract: Let $mathfrakg$ be a hyperbolic Kac-Moody algebra of rank $2$. We give a polyhedral realization of the crystal basis for the extremal weight module of extremal weight $lambda$, where $lambda$ is an integral weight whose Weyl group orbit has neither a dominant integral weight nor an antidominant integral weight.

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)

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