Gelfand-Tsetlin modules for gl(m|n)

Author(s)

Futorny, Vyacheslav ; Serganova, Vera ; Zhang, Jian

• Document type: Journal article
• Source: MATHEMATICAL RESEARCH LETTERS; v. 28, n. 5, p. 40-pg., 2021-01-01.

Abstract

We address the problem of classifying irreducible Gelfand-Tsetlin modules for gl(m|n) and show that it reduces to the classification of Gelfand-Tsetlin modules for the even part. We also give an explicit tableaux construction and the irreducibility criterion for the class of quasi typical and quasi covariant Gelfand-Tsetlin modules which includes all essentially typical and covariant tensor finite dimensional modules. In the quasi typical case new irreducible representations are infinite dimensional gl(m|n)-modules which are isomorphic to the parabolically induced (Kac) modules. (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: 18/23690-6 - Structures, representations, and applications of algebraic systems
• Grantee: Ivan Chestakov
• Support Opportunities: Research Projects - Thematic Grants