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 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.
Cite this article
Shun-Jen Cheng, Weiqiang Wang, Brundan–Kazhdan–Lusztig and Super Duality Conjectures. Publ. Res. Inst. Math. Sci. 44 (2008), no. 4, pp. 1219–1272DOI 10.2977/PRIMS/1231263785