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Journal of Lie Theory 29 (2019), No. 1, 277--302
Copyright Heldermann Verlag 2019

Essential Signatures and Monomial Bases for Bn and Dn

Andrei A. Gornitskii
National Research University, Moscow Power Engineering Institute, Krasnokazarmennaya 14, Moscow 111250, Russia

In the representation theory of simple Lie algebras, we consider the problem of constructing a monomial basis in an arbitrary irreducible finite-dimensional highest weight module. We construct a PBW-type basis in every finite-dimensional representation of Bn and Dn and we describe the associated semigroup of essential signatures. These bases are parameterized by integer points in some polytopes. We give the inequalities defining these polytopes.

Keywords: Simple Lie algebra, irreducible representation, weight basis, essential signature.

MSC: 17B10, 17B20

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