The PBW filtration and convex polytopes in type B

DOI10.1016/J.JPAA.2018.03.009zbMATH Open1464.17011arXiv1504.06522OpenAlexW2963316866MaRDI QIDQ1672028

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Publication date: 7 September 2018

Published in: (Search for Journal in Brave)

Abstract: We study the PBW filtration on irreducible finite--dimensional representations for the Lie algebra of type $t{B}_n$. We prove in several cases, including all multiples of the adjoint representation and all irreducible finite--dimensional representations for $t{B}_3$, that there exists a normal polytope such that the lattice points of this polytope parametrize a basis of the corresponding associated graded space. As a consequence we obtain several classes of favourable modules and graded combinatorial character formulas.

Full work available at URL: https://arxiv.org/abs/1504.06522

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