Brundan-Kazhdan-Lusztig conjecture for general linear 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.

64 pages, Notes in the Introduction and Remark 3.14 added

References in corpus (3)

• Super duality and irreducible characters of ortho-symplectic Lie superalgebras
• Irreducible Characters of General Linear Superalgebra and Super Duality
• Categorification of integrable representations of quantum groups

Cited by in corpus (11)

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• Tilting modules for classical Lie superalgebras
• The primitive spectrum of basic classical Lie superalgebras
• Integrable $sl(\infty )$-modules and Category $\mathcal{O}$ for $\mathfrak{gl}(m|n)$
• Reduction method for representations of queer Lie superalgebras
• An inversion formula for some Fock spaces
• Character formulae for queer Lie superalgebras and canonical bases of types $A/C$
• Kac-Wakimoto character formula for ortho-symplectic Lie superalgebras
• Characters for Projective Modules in the BGG Category O for General Linear Lie Superalgebras
• Characters for Projective Modules in the BGG Category $\mathcal{O}$ for the Orthosymplectic Lie Superalgebra $\mathfrak{osp}(3|4)$
• Character formulae in category $\mathcal{O}$ for exceptional Lie superalgebra $G(3)$