Howe duality and Kostant Homology Formula for infinite-dimensional Lie superalgebras

Abstract

Using Howe duality we compute explicitly Kostant-type homology groups for a wide class of representations of the infinite-dimensional Lie superalgebra ${\widehat{\mathfrak{gl}}}_{\infty |\infty }$ and its classical subalgebras at positive integral levels. We also obtain Kostant-type homology formulas for the Lie algebra $widehat{\mathfrak{gl}}_{\infty }$ at negative integral levels. We further construct resolutions in terms of generalized Verma modules for these representations.

References in corpus (2)

• Integrable highest weight modules over affine superalgebras and Appell's function
• Infinite-dimensional Lie superalgebras and hook Schur functions

Cited by in corpus (9)

• Super duality and irreducible characters of ortho-symplectic Lie superalgebras
• Irreducible Characters of General Linear Superalgebra and Super Duality
• Kostant homology formulas for oscillator modules of Lie superalgebras
• Super duality and Crystal bases for quantum orthosymplectic superalgebras
• Super duality and Crystal bases for quantum orthosymplectic superalgebras II
• Irreducible Characters of Kac-Moody Lie superalgebras
• Kac-Wakimoto character formula for ortho-symplectic Lie superalgebras
• Affinization of $q$-oscillator representations of $U_q({\mathfrak{gl}}_n)$
• Crystal bases of parabolic Verma modules over the quantum orthosymplectic superalgebras