Lie Superalgebras and Generalized Kazhdan-Lusztig Polynomials

Abstract

We present `liesuperalg` a SageMath package for representation-theoretic calculations involving Lie superalgebras in Type A. Our package introduces functionality to calculate invariants of weights and produce the associated cup diagrams. We expose functionality to calculate characters of irreducible representations, work with combinatorics of generalized Kazhdan-Lusztig polynomials, and determine composition factor multiplicities of indecomposable modules. Our package implements an algorithm to decompose arbitrary modules in terms of irreducible ones in the Grothendeick group of Lie superalgebra representations.