Irreducible Characters of Kac-Moody Lie superalgebras

Abstract

Generalizing the super duality formalism for finite-dimensional Lie superalgebras of type $ABCD$, we establish an equivalence between parabolic BGG categories of a Kac-Moody Lie superalgebra and a Kac-Moody Lie algebra. The characters for a large family of irreducible highest weight modules over a symmetrizable Kac-Moody Lie superalgebra are then given in terms of Kazhdan-Lusztig polynomials for the first time. We formulate a notion of integrable modules over a symmetrizable Kac-Moody Lie superalgebra via super duality, and show that these integrable modules form a semisimple tensor subcategory, whose Littlewood-Richardson tensor product multiplicities coincide with those in the Kac-Moody algebra setting.

28 pages

References in corpus (3)

• Quantum Supergroups III. Twistors
• Howe duality and Kostant Homology Formula for infinite-dimensional Lie superalgebras
• Generalised Jantzen filtration of Lie superalgebras II: the exceptional cases

Cited by in corpus (5)

• Superspace conformal field theory
• Super duality and Crystal bases for quantum orthosymplectic superalgebras II
• Blocks and characters of $G(3)$-modules of non-integral weights
• A study on free roots of Borcherds-Kac-Moody Lie Superalgebras
• A family of representations of the affine Lie superalgebra $\widehat{{\mathfrak{gl}}_{m|n}}(\mathbb{C})$