Gelfand-Tsetlin modules for gl(m|n)

作者：Futorny, Vyacheslav^*; Serganova, Vera; Zhang, Jian

来源：Mathematical Research Letters, 2021, 28(5): 1379-1418.

• FINITE-DIMENSIONAL REPRESENTATIONS
• TYPICAL REPRESENTATIONS
• CLASSICAL MECHANICS
• ZEITLIN THEORY
• PERSPECTIVE
• CHARACTERS

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.