Brundan-Kazhdan-Lusztig conjecture for general linear Lie superalgebras

TL;DR

This paper proves Brundan's Kazhdan-Lusztig type conjecture for characters of irreducible and tilting modules in the BGG category of general linear Lie superalgebras, confirming a long-standing hypothesis.

Contribution

It establishes the conjecture and its variants for all Borel subalgebras in full generality, advancing the understanding of representation theory for Lie superalgebras.

Findings

Proof of Brundan's conjecture for all Borel subalgebras

Validation of the conjecture's variants

Extension of Kazhdan-Lusztig theory to Lie superalgebras

Abstract

In the framework of canonical and dual canonical bases of Fock spaces, Brundan in 2003 formulated a Kazhdan-Lusztig type conjecture for the characters of the irreducible and tilting modules in the BGG category for the general linear Lie superalgebra for the first time. In this paper, we prove Brundan's conjecture and its variants associated to all Borel subalgebras in full generality.