Cohomology of generalized supergrassmannians and character formulae for basic classical Lie superalgebras

TL;DR

This paper employs geometric methods inspired by Borel-Weil-Bott theory to compute characters of all finite-dimensional simple modules over basic classical Lie superalgebras.

Contribution

It introduces a geometric approach to determine characters of simple modules for basic classical Lie superalgebras, extending previous algebraic techniques.

Findings

Explicit character formulas for all finite-dimensional simple modules.

Application of geometric methods to Lie superalgebra representation theory.

Enhanced understanding of the structure of basic classical Lie superalgebras.

Abstract

In this paper, we use geometrical methods adapted from the Borel-Weil-Bott theory to compute the character of every finite dimensional simple module over a basic classical Lie superalgebra.