324 research outputs found
Brundan-Kazhdan-Lusztig and super duality conjectures
We formulate a general super duality conjecture on connections between
parabolic categories O of modules over Lie superalgebras and Lie algebras of
type A, based on a Fock space formalism of their Kazhdan-Lusztig theories which
was initiated by Brundan. We show that the Brundan-Kazhdan-Lusztig (BKL)
polynomials for Lie superalgebra gl(m|n) in our parabolic setup can be
identified with the usual parabolic Kazhdan-Lusztig polynomials. We establish
some special cases of the BKL conjecture on the parabolic category O of
gl(m|n)-modules and additional results which support the BKL conjecture and
super duality conjecture.Comment: v2, 44 pages, mild changes, clarifications on Introduction and other
place
Character formulae in category for exceptional Lie superalgebra
We classify the blocks, compute the Verma flags of tilting and projective
modules in the BGG category for the exceptional Lie superalgebra
. The projective injective modules in are classified. We
also compute the Jordan-H\"older multiplicities of the Verma modules in
.Comment: 28 page
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