Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra 𝔤𝔩(𝔪|𝔫)

Abstract

We compute the characters of the finite dimensional irreducible representations of the Lie superalgebra g l ( m | n ) \mathfrak {gl}(m|n) , and determine Ext {\operatorname {Ext}} ’s between simple modules in the category of finite dimensional representations. We formulate conjectures for the analogous results in category O \mathcal O . The combinatorics parallels the combinatorics of certain canonical bases over the Lie algebra g l ( ∞ ) \mathfrak {gl}(\infty ) .