Publications (27)
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…
IntroSurvey of representation theory
Nicolas Libedinsky
There could be thousands of Introductions/Surveys of representation theory, given that it is an enormous field. This is just one of them, quite personal and informal. It has an inc…
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…
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…
Sur la catégorie des bimodules de Soergel
Nicolas Libedinsky
The Soergel category B of a Coxeter system (W,S) is a bimodule category over a polynomial algebra on which W acts. It's a categorification of the Hecke Algebra of (W,S). In this ar…
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…
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…
Light leaves and Lusztig's conjecture
Nicolas Libedinsky
We introduce the Double leaves basis, a combinatorial basis for the Hom spaces between two Bott-Samelson-Soergel bimodules. As an application we give a combinatorial algorithm to f…
Shape and class of Bruhat Intervals
Gaston Burrull, Nicolas Libedinsky, Rodrigo Villegas
We study Bruhat intervals in affine Weyl groups by viewing them as regions of alcoves. In type we show that each interval coincides with a generalized permutohedr…
Equivalences entre conjectures de Soergel
Nicolas Libedinsky
Soergel's category B_k(V) over a field k is defined from a Coxeter system (W,S) and a k-linear representation V of W. It's a categorification of the Hecke algebra of (W,S). In this…
Standard objects in 2-braid groups
Nicolas Libedinsky, Geordie Williamson
For any Coxeter system we establish the existence (conjectured by Rouquier) of analogues of standard and costandard objects in 2-braid groups. This generalizes a known extension va…
A non-perverse Soergel bimodule in type A
Nicolas Libedinsky, Geordie Williamson
A basic question concerning indecomposable Soergel bimodules is to understand their endomorphism rings. In characteristic zero all degree-zero endomorphisms are isomorphisms (a fac…
New bases of some Hecke algebras via Soergel bimodules
Nicolas Libedinsky
For extra-large Coxeter systems (m(s,r)>3), we construct a natural and explicit set of Soergel bimodules D={D_w}_{w\in W} such that each D_w contains as a direct summand (or is equ…
Presentation of right-angled Soergel categories by generators and relations
Nicolas Libedinsky
Soergel bimodule category B is a categorification of the Hecke algebra of a Coxeter system (W,S). We find a presentation of B (as a tensor category) by generators and relations whe…
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 size of Bruhat intervals
Federico Castillo, Damian de la Fuente, Nicolas Libedinsky +1
For affine Weyl groups and elements associated to dominant coweights, we present a convex geometry formula for the size of the corresponding lower Bruhat intervals. Extensive compu…
Paper BOAT
Federico Castillo, Damian de la Fuente, Nicolas Libedinsky +1
We derive a formula for computing the size of lower Bruhat intervals for elements in the dominant cone of an affine Weyl group of type . This enumeration problem is reduced to c…
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…
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…
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…
The anti-spherical category
Nicolas Libedinsky, Geordie Williamson
We study a diagrammatic categorification (the "anti-spherical category") of the anti-spherical module for any Coxeter group. We deduce that Deodhar's (sign) parabolic Kazhdan-Luszt…
Kazhdan-Lusztig polynomials and subexpressions
Nicolas Libedinsky, Geordie Williamson
We refine an idea of Deodhar, whose goal is a counting formula for Kazhdan-Lusztig polynomials. This is a consequence of a simple observation that one can use the solution of Soerg…
-Jones-Wenzl idempotents
Gaston Burrull, Nicolas Libedinsky, Paolo Sentinelli
For a prime number and any natural number we introduce, by giving an explicit recursive formula, the -Jones-Wenzl projector , an element of the…
Bruhat intervals that are large hypercubes
Jordan Ellenberg, Nicolas Libedinsky, David Plaza +2
We study the question of finding big Bruhat intervals that are poset hypercubes in the symmetric group . Using permutations suggested by AlphaEvolve (an evolutionary coding ag…
Soohak: A Mathematician-Curated Benchmark for Evaluating Research-level Math Capabilities of LLMs
Guijin Son, Seungone Kim, Catherine Arnett +73
Following the recent achievement of gold-medal performance on the IMO by frontier LLMs, the community is searching for the next meaningful and challenging target for measuring LLM…
Soergel bimodules for universal Coxeter groups
Ben Elias, Nicolas Libedinsky
We produce an explicit recursive formula which computes the idempotent projecting to any indecomposable Soergel bimodule for a universal Coxeter system. This gives the exact set of…
Gentle introduction to Soergel bimodules I: The basics
Nicolas Libedinsky
This paper is the first of a series of introductory papers on the fascinating world of Soergel bimodules. It is combinatorial in nature and should be accessible to a broad audience…