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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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.

Item Type: Journal Article
Creators:
CreatorsEmailORCIDORCID Put Code
Molev, AlexanderUNSPECIFIEDorcid.org/0000-0002-7321-1592UNSPECIFIED
Yakimova, OksanaUNSPECIFIEDUNSPECIFIEDUNSPECIFIED
URN: urn:nbn:de:hbz:38-329020
DOI: 10.1007/s00031-020-09585-1
Journal or Publication Title: Transform. Groups
Publisher: SPRINGER BIRKHAUSER
Place of Publication: NEW YORK
ISSN: 1531-586X
Language: English
Faculty: Unspecified
Divisions: Unspecified
Subjects: no entry
Uncontrolled Keywords:
KeywordsLanguage
DEGENERATIONS; MODULESMultiple languages
MathematicsMultiple languages
URI: http://kups.ub.uni-koeln.de/id/eprint/32902

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