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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Gelfand-Tsetlin representations of finite W-algebras

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Futorny, Vyacheslav [1] ; Ramirez, Luis Enrique [2] ; Zhang, Jian [1]
Total Authors: 3
[1] Univ Sao Paulo, Inst Math & Stat, Caixa Postal 66281, BR-05315970 Sao Paulo - Brazil
[2] Univ Fed ABC, Santo Andre, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Journal of Pure and Applied Algebra; v. 224, n. 5 MAY 2020.
Web of Science Citations: 0

We construct explicitly a large family of new simple modules for an arbitrary finite W-algebra of type A. A basis of these modules is given by the Gelfand-Tsetlin tableaux whose entries satisfy certain sets of relations. Characterization and an effective method of constructing such admissible relations are given. In particular we describe a family of simple infinite dimensional highest weight relation modules. We also prove a sufficient condition for the simplicity of tensor product of two highest weight relation modules and establish the simplicity of the tensor product any number of relation modules with generic highest weights. This extends the results of Molev to infinite dimensional highest weight modules. (C) 2019 Elsevier B.V. All rights reserved. (AU)

FAPESP's process: 15/05927-0 - Quantum determinants and categorification of quantum groups
Grantee:Jian Zhang
Support Opportunities: Scholarships in Brazil - Post-Doctoral
FAPESP's process: 14/09310-5 - Algebraic structures and their representations
Grantee:Vyacheslav Futorny
Support Opportunities: Research Projects - Thematic Grants
FAPESP's process: 18/17955-7 - Tableaux realization of cuspidal modules for Simple Lie algebras
Grantee:Luis Enrique Ramírez
Support Opportunities: Regular Research Grants