Brundan-Kazhdan-Lusztig and Super Duality Conjectures

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 gl(m|n) in our parabolic setup can be identified with the usual parabolic Kazhda...

Perverse Sheaves and the Kazhdan-lusztig Conjectures

Kazhdan-lusztig Cells

These are notes for a talk on Kazhdan-Lusztig Cells for Hecke Algebras. In this talk, we construct the Kazhdan-Lusztig basis for the Hecke algebra associated to an arbitrary Coxeter group, in full multiparameter generality. We then use this basis to construct a partition of the Coxeter group into the Kazhdan-Lusztig cells and describe the corresponding cell representations. Finally, we speciali...

Relative Kazhdan–lusztig Cells

In this paper, we study the Kazhdan–Lusztig cells of a Coxeter group W in a “relative” setting, with respect to a parabolic subgroup WI ⊆ W . This relies on a factorization of the Kazhdan–Lusztig basis {Cw} of the corresponding (multi-parameter) Iwahori–Hecke algebra with respect to WI . We obtain two applications to the “asymptotic case” in type Bn, as introduced by Bonnafé and Iancu: we show ...

Kazhdan-Lusztig polynomials of matroids: a survey of results and conjectures

We report on various results, conjectures, and open problems related to KazhdanLusztig polynomials of matroids. We focus on conjectures about the roots of these polynomials, all of which appear here for the first time.