Publication Date:
2014-12-27
Description:
Generalizing the super duality formalism for finite-dimensional Lie superalgebras of type $ABCD$ , we establish an equivalence between parabolic Bernstein-Gelfand-Gelfand (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 Lie algebra setting.
Print ISSN:
0024-6115
Electronic ISSN:
1460-244X
Topics:
Mathematics
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