Publications (17)
On reduced expressions for core double cosets
Ben Elias, Hankyung Ko, Nicolas Libedinsky +1
The notion of a reduced expression for a double coset in a Coxeter group was introduced by Williamson, and recent work of Elias and Ko has made this theory more accessible and comb…
Bases of the Intersection Cohomology of Grassmannian Schubert Varieties
Leonardo Patimo
The parabolic Kazhdan-Lusztig polynomials for Grassmannians can be computed by counting Dyck partitions. We "lift" this combinatorial formula to the corresponding category of singu…
The charge statistic in type A via the Affine Grassmannian
Leonardo Patimo
We give a new construction of Lascoux-Schüetzenberger's charge statistic in type A which is motivated by the geometric Satake equivalence. We obtain a new formula for the charge s…
Subexpressions and the Bruhat order for double cosets
Ben Elias, Hankyung Ko, Nicolas Libedinsky +1
The Bruhat order on a Coxeter group is often described by examining subexpressions of a reduced expression. We prove that an analogous description applies to the Bruhat order on do…
A combinatorial formula for the coefficient of in Kazhdan-Lusztig polynomials
Leonardo Patimo
We propose a combinatorial interpretation of the coefficient of in Kazhdan- Lusztig polynomials and we prove it for finite simply-laced Weyl groups.
On the affine Hecke category for
Nicolas Libedinsky, Leonardo Patimo
We study the diagrammatic Hecke category associated with the affine Weyl group of type . More precisely we find a (surprisingly simple) basis for the Hom spaces betwee…