Irreducible Characters of General Linear Superalgebra and Super Duality

Abstract

We develop a new method to solve the irreducible character problem for a wide class of modules over the general linear superalgebra, including all the finite-dimensional modules, by directly relating the problem to the classical Kazhdan-Lusztig theory. We further verify a parabolic version of a conjecture of Brundan on the irreducible characters in the BGG category $\mc{O}$ of the general linear superalgebra. We also prove the super duality conjecture.

References in corpus (3)

• A BGG-type resolution for tensor modules over general linear superalgebra
• Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra q(n)
• Howe duality and Kostant Homology Formula for infinite-dimensional Lie superalgebras

Cited by in corpus (24)

• Stability patterns in representation theory
• Tensor product categorifications and the super Kazhdan-Lusztig conjecture
• Super duality and irreducible characters of ortho-symplectic Lie superalgebras
• Brundan-Kazhdan-Lusztig conjecture for general linear Lie superalgebras
• Super duality and Crystal bases for quantum orthosymplectic superalgebras
• Finite-dimensional half-integer weight modules over queer Lie superalgebras
• Correspondences of categories for subregular W-algebras and principal W-superalgebras
• Character and dimension formulae for queer Lie superalgebra
• Irreducible Characters of Kac-Moody Lie superalgebras
• Generalised Verma modules for the orthosymplectic Lie superalgebra osp(k|2)
• Complexity and module varieties for classical Lie superalgebras
• Kac-Wakimoto character formula for ortho-symplectic Lie superalgebras
• Higher level $q$-oscillator representations for $U_q(C_n^{(1)}),U_q(C^{(2)}(n+1))$ and $U_q(B^{(1)}(0,n))$
• Highest weight categories arising from Khovanov's diagram algebra IV: the general linear supergroup
• Generalised Jantzen filtration of Lie superalgebras II: the exceptional cases
• Affinization of $q$-oscillator representations of $U_q({\mathfrak{gl}}_n)$
• Dualities for Lie superalgebras
• Solutions of super Knizhnik-Zamolodchikov equations
• Gaudin Hamiltonians on unitarizable modules over classical Lie (super)algebras
• Generalised Jantzen filtration of Lie superalgebras I
• Quadratic and cubic Gaudin Hamiltonians and super Knizhnik-Zamolodchikov equations for general linear Lie superalgebras
• $R$ matrix for generalized quantum group of type $A$
• Super duality for quantum affine algebras of type $A$
• Littlewood identity and Crystal bases