Geometric construction of Gelfand-Tsetlin modules over simple Lie algebras

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Author(s):	Futorny, Vyacheslav ^[1] ; Krizka, Libor ^[1] Total Authors: 2
Affiliation:	^[1] Univ Sao Paulo, Inst Matemat & Estat, Caixa Postal 66281, BR-05315970 Sao Paulo - Brazil Total Affiliations: 1
Document type:	Journal article
Source:	Journal of Pure and Applied Algebra; v. 223, n. 11, p. 4901-4924, NOV 2019.
Web of Science Citations:	0
Abstract
In the present paper we describe a new class of Gelfand-Tsetlin modules for an arbitrary complex simple finite-dimensional Lie algebra g and give their geometric realization as the space of `delta-functions' on the flag manifold G/B supported at the 1-dimensional submanifold. When g = sl(n, C) (or gl(n, C)) these modules form a subclass of Gelfand-Tsetlin modules with infinite-dimensional weight subspaces. We discuss their properties and describe the simplicity criterion for these modules in the case of the Lie algebra sl(3, C). (C) 2019 Elsevier B.V. All rights reserved. (AU)

FAPESP's process:	14/09310-5 - Algebraic structures and their representations
Grantee:	Vyacheslav Futorny
Support Opportunities:	Research Projects - Thematic Grants