Chih-Whi Chen
Published 2023-09-13Version 1
We study the classical problem of Kostant for Whittaker modules over Lie algebras and Lie superalgebras. We give a sufficient condition for a positive answer to Kostant's problem for the standard Whittaker modules over reductive Lie algebras. Under the same condition, the positivity of the answer for simple Whittaker modules is reduced to that for simple highest weight modules. We develop several reduction results to reduce the Kostant's problem for standard and simple Whittaker modules over a type I Lie superalgebra to that for the corresponding Whittaker modules over the even part of this Lie superalgebra.
Gelfand-Tsetlin modules for Lie algebras of rank $2$
Polynomial Representations of the Lie Superalgebra osp(1|2n)
Classification of Harish-Chandra modules over some Lie algebras related to the Virasoro algebra
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