11 citations · 30 across the 12 of their papers we have counts for
14 papers
Positivity of Pre-Canonical Bases for Spherical Hecke Algebras
David Plaza, Yamil Sagurie
We introduce a new algorithm for computing Kostka-Foulkes polynomials. It arises from a combinatorial procedure that computes the transition coefficients between successive pre-can…
A differential characterization of volume polynomials of permutohedra
Tristram Bogart, Federico Castillo, Damián de la Fuente +1
We study a graded vector space of polynomials associated to a square matrix, defined by a finite difference condition along the rows. We show this space coincides with one defined…
Combinatorial invariance conjecture for
Gaston Burrull, Nicolas Libedinsky, David Plaza
The combinatorial invariance conjecture (due independently to G. Lusztig and M. Dyer) predicts that if and are isomorphic Bruhat posets (of possibly different Cox…
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…
Kazhdan-Lusztig polynomials for
Karina Batistelli, Aram Bingham, David Plaza
Kazhdan and Lusztig define, for an arbitrary Coxeter system , a family of polynomials indexed by pairs of elements of . Despite their relevance and elementary definition,…
The nil-blob algebra: An incarnation of type Soergel calculus and of the truncated blob algebra
Diego Lobos, David Plaza, Steen Ryom-Hansen
We introduce a type analogue of the nil Temperley-Lieb algebra in terms of generators and relations, that we call the (extended) nil-blob algebra. We show that this algebra is…
Type Temperley-Lieb algebra quotients and Catalan combinatorics
Sadek Al Harbat, Camilo González, David Plaza
We study some algebraic and combinatorial features of two algebras that arise as quotients of Temperley-Lieb algebras of type , namely, the two-boundary Temperley-Lieb a…
Blob algebra and two-color Soergel calculus
Jorge Espinoza, David Plaza
In 2003, Martin and Woodcock noticed a connection between the representation theory of the blob algebra and the Kazhdan--Lusztig polynomials associated with the infinite dihedral g…
Diagrammatics for Kazhdan-Lusztig R-polynomials
David Plaza
Let be an arbitrary Coxeter system. We introduce a family of polynomials, , indexed by pairs formed by an…
Blob algebra approach to modular representation theory
Nicolas Libedinsky, David Plaza
Two decades ago P. Martin and D. Woodcock made a surprising and prophetic link between statistical mechanics and representation theory. They observed that the decomposition numbers…
Categorification of a recursive formula for Kazhdan-Lusztig polynomials
David Plaza
We obtain explicit branching rules for graded cell modules and graded simple modules over the endomorphism algebra of a Bott-Samelson bimodule. These rules allow us to categorify a…
Graded cellularity and the Monotonicity Conjecture
David Plaza
The graded cellularity of Libedinsky Double Leaves, which form a basis for the endomorphism ring of the Bott_Samelson_Soergel bimodules, allows us to view the Kazhdan_Lusztig polyn…
Graded decomposition numbers for the blob algebra
David Plaza
We give a closed formula for the graded decomposition numbers of the blob algebra over a field of characteristic zero at a root of unity.
Graded cellular bases for Temperley-Lieb algebras of type A and B
David Plaza, Steen Ryom-Hansen
We show that the Temperley-Lieb algebra of type and the blob algebra (also known as the Temperley-Lieb algebra of type ) at roots of unity are -graded algebras.…