Kac-Wakimoto character formula for ortho-symplectic Lie superalgebras

TL;DR

This paper proves the Kac-Wakimoto character formula for finite-dimensional tame modules over ortho-symplectic Lie superalgebras, connecting it to super Jacobi polynomials and confirming a longstanding conjecture.

Contribution

It establishes the Kac-Wakimoto conjecture for ortho-symplectic Lie superalgebras and links the character formula to super Jacobi polynomials.

Findings

Characters of tame modules are given by the Kac-Wakimoto formula

The Kac-Wakimoto formula is related to super Jacobi polynomials

Super Jacobi polynomials give super characters up to a sign

Abstract

We classify finite-dimensional tame modules over the ortho-symplectic Lie superalgebras. For these modules we show that their characters are given by the Kac-Wakimoto character formula, thus establishing the Kac-Wakimoto conjecture for the ortho-symplectic Lie superalgebras. We further relate the Kac-Wakimoto formula to the super Jacobi polynomials of Sergeev and Veselov, and show that these polynomials, up to a sign, give the super characters for these tame modules.