Combinatorics and Algebraic Topology of Configurations

Special matchings and parabolic Kazhdan-Lusztig polynomials

speaker: Mario Marietti (Università Politecnica delle Marche)

abstract: We show how the combinatorial concept of special matching can be used to compute the parabolic Kazhdan-Lusztig polynomials of doubly laced Coxeter groups and of dihedral Coxeter groups. In particular, for this class of groups which includes all Weyl groups, we generalize to the parabolic setting certain results of Brenti, Caselli, and myself. As a consequence, the parabolic Kazhdan-Lusztig polynomial indexed by $u$ and $v$ depends only on the poset structure of the lower Bruhat interval (e,v) and on which elements of that interval are minimal coset representatives.​

timetable:
Tue 17 Feb, 10:40 - 11:20, Aula Dini
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