7 citations · 8 across the 11 of their papers we have counts for
13 papers
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 st…
The atomic Leibniz rule
Ben Elias, Hankyung Ko, Nicolas Libedinsky +1
The Demazure operator associated to a simple reflection satisfies the twisted Leibniz rule. In this paper we introduce a generalization of the twisted Leibniz rule for the Demazure…
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…
Singular Light Leaves
Ben Elias, Hankyung Ko, Nicolas Libedinsky +1
For any Coxeter system we introduce the concept of singular light leaves, answering a question of Williamson raised in 2008. They provide a combinatorial basis for Hom spaces betwe…
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…
Demazure operators for double cosets
Ben Elias, Hankyung Ko, Nicolas Libedinsky +1
For any Coxeter system, and any double coset for two standard parabolic subgroups, we introduce a Demazure operator. These operators form a basis for morphism spaces in a category…
Atoms and charge in type
Leonardo Patimo, Jacinta Torres
We construct atomic decompositions for crystals of type and define a charge statistic on them, thus providing positive combinatorial formulas for Kostka-Foulkes polynomials…
Charges via the Affine Grassmannian
Leonardo Patimo
We give a new construction of Lascoux-Schützenberger's charge statistic in type A which is motivated by the geometric Satake equivalence We obtain a new formula for the charge stat…
Pre-canonical bases on affine Hecke algebras
Nicolas Libedinsky, Leonardo Patimo, David Plaza
For any affine Weyl group, we introduce the pre-canonical bases. They are a set of bases (where is the height of the highest root) of the…
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…
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…
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.
The Hard Lefschetz Theorem in positive characteristic for the Flag Varieties
Leonardo Patimo
For a given flag variety, we characterize the primes for which there exists a weight such that the Hard Lefschetz Theorem holds for multiplication by on the cohomology…