Gelfand-Tsetlin representations of finite W-algebras

Author(s)

Futorny, Vyacheslav ^[1] ; Ramirez, Luis Enrique ^[2] ; Zhang, Jian ^[1]

Affiliation

^[1] Univ Sao Paulo, Inst Math & Stat, Caixa Postal 66281, BR-05315970 Sao Paulo - Brazil

^[2] Univ Fed ABC, Santo Andre, SP - Brazil

• Document type: Journal article
• Source: Journal of Pure and Applied Algebra; v. 224, n. 5 MAY 2020.
• Web of Science Citations: 0

Abstract

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