MONOMIAL BASES AND BRANCHING RULES - Kölner UniversitätsPublikationsServer

Molev, Alexander ORCID: 0000-0002-7321-1592 and Yakimova, Oksana . MONOMIAL BASES AND BRANCHING RULES. Transform. Groups. NEW YORK: SPRINGER BIRKHAUSER. ISSN 1531-586X

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DOI:10.1007/s00031-020-09585-1

Abstract

Following a question of Vinberg, a general method to construct monomial bases for finite-dimensional irreducible representations of a reductive Lie algebra g was developed in a series of papers by Feigin, Fourier, and Littelmann. Relying on this method, we construct monomial bases of multiplicity spaces associated with the restriction of the representation to a reductive subalgebra g 0 subset of g. As an application, we produce new monomial bases for representations of the symplectic Lie algebra associated with a natural chain of subalgebras. One of our bases is related via a triangular transition matrix to a suitably modified version of the basis constructed earlier by the first author. In type A, our approach shows that the Gelfand{Tsetlin basis and the canonical basis of Lusztig have a common PBW-parameterisation. This implies that the transition matrix between them is triangular. We show also that a similar relationship holds for the Gelfand{Tsetlin and the Littelmann bases in type A.

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Journal Article

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