Super duality and irreducible characters of ortho-symplectic Lie superalgebras

TL;DR

This paper introduces a super duality connecting ortho-symplectic Lie superalgebras with classical Lie algebras, solving the irreducible character problem using Kazhdan-Lusztig polynomials.

Contribution

It establishes a super duality framework that fully characterizes irreducible modules of ortho-symplectic Lie superalgebras via classical Lie algebra techniques.

Findings

Super duality links categories O of superalgebras and classical Lie algebras.

Complete solution to irreducible character problem for ortho-symplectic superalgebras.

Irreducible characters expressed through Kazhdan-Lusztig polynomials.

Abstract

We formulate and establish a super duality which connects parabolic categories $O$ between the ortho-symplectic Lie superalgebras and classical Lie algebras of $BCD$ types. This provides a complete and conceptual solution of the irreducible character problem for the ortho-symplectic Lie superalgebras in a parabolic category $O$, which includes all finite-dimensional irreducible modules, in terms of classical Kazhdan-Lusztig polynomials.