Twisting Functors and Generalized Verma modules

TL;DR

This paper investigates how twisting functors affect the characters of generalized Verma modules in reductive Lie algebras and extends these results to Lie superalgebras, generalizing previous findings.

Contribution

It provides new conditions ensuring the well-behaved nature of characters under twisting functors and extends results to Lie superalgebras.

Findings

Character of generalized Verma modules is well-behaved under certain twisting functors.

Results extended to basic classical simple Lie superalgebras.

Generalization of previous work on twisting Verma modules.

Abstract

Let $\mathfrak{g}$ be a reductive Lie algebra. We give a condition that ensures that the character of a generalized Verma module is well-behaved under a twisting functor. We show that a similar result holds for basic classical simple Lie superalgebras, and generalize a result from \cite{CM} about twisting Verma modules.