Super duality and irreducible characters of ortho-symplectic Lie superalgebras

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.

30 pages, Section 5 rewritten and shortened

References in corpus (3)

• Irreducible Characters of General Linear Superalgebra and Super Duality
• Kostant homology formulas for oscillator modules of Lie superalgebras
• Howe duality and Kostant Homology Formula for infinite-dimensional Lie superalgebras

Cited by in corpus (22)

• Stability patterns in representation theory
• Superspace conformal field theory
• Brundan-Kazhdan-Lusztig conjecture for general linear Lie superalgebras
• Whittaker modules for classical Lie superalgebras
• Tilting modules for classical Lie superalgebras
• Super duality and Crystal bases for quantum orthosymplectic superalgebras
• Super duality and Crystal bases for quantum orthosymplectic superalgebras II
• 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
• Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras
• Recent advances and open questions on the susy structure of the chiral de Rham Complex
• Higher level $q$-oscillator representations for $U_q(C_n^{(1)}),U_q(C^{(2)}(n+1))$ and $U_q(B^{(1)}(0,n))$
• Kac-Wakimoto character formula for ortho-symplectic Lie superalgebras
• Joseph-like ideals and harmonic analysis for osp(m|2n)
• Crystal base of the negative half of the quantum superalgebra $U_q(\mathfrak{gl}(m|n))$
• Gaudin Hamiltonians on unitarizable modules over classical Lie (super)algebras
• Solutions of super Knizhnik-Zamolodchikov equations
• Characters for Projective Modules in the BGG Category $\mathcal{O}$ for the Orthosymplectic Lie Superalgebra $\mathfrak{osp}(3|4)$
• Quadratic and cubic Gaudin Hamiltonians and super Knizhnik-Zamolodchikov equations for general linear Lie superalgebras
• Character formulae in category $\mathcal{O}$ for exceptional Lie superalgebra $G(3)$