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 superalgebragl(m|n)\mathfrak {gl}(m|n), and determineExt{\operatorname {Ext}}’s between simple modules in the category of finite dimensional representations. We formulate conjectures for the analogous results in categoryO\mathcal O. The combinatorics parallels the combinatorics of certain canonical bases over the Lie algebragl(∞)\mathfrak {gl}(\infty ).