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arXiv · 0705.0050

Brundan-Kazhdan-Lusztig and super duality conjectures

Shun-Jen Cheng·Weiqiang Wang
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Abstract

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.

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BibTeXRIS

Shun-Jen Cheng, Weiqiang Wang. 2008-04-16. Brundan-Kazhdan-Lusztig and super duality conjectures. https://arxiv.org/abs/0705.0050

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