Constructs monomial bases in finite-dimensional representations of Bn and Dn, indicating their implications for representation theory.
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 B n and D n 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.
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A. A. Gornitskii (2019) studied this question.
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