• Date:  2024-01-31 (Wed) 15:30  ~ 17:00 
• Place:  1423 (KIAS)
• Speaker:  Chen, Chih-Whi (National Central University)
• Title:  Kostant’s problem for Whittaker modules over Lie superalgebras
• Abstract: Let g be a reductive complex finite dimensional Lie algebra. The classical problem of Kostant asks for which g-modules M the algebra of adjointly locally finite linear endomorphisms of M coincides with the image of the universal enveloping algebra U(g) under the representation map. The positive answer to Kostant’s problem provides important tools in the study of equivalences of various categories for Lie (super)algebra modules. In this talk, we introduce several reduction methods to reduce the answer to this problem for certain simple and standard Whittaker modules over a reductive Lie algebra to the corresponding answer for some highest weight modules over this Lie algebra. We reduce the answer to this problem for various Whittaker modules over a quasireductive Lie superalgebra of type I to the corresponding answer for Whittaker modules over the even part of this Lie superalgebra.