Nicolás Libedinsky
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View article: Paper BOAT
Paper BOAT Open
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 $A$. This enumeration problem is reduced to counting lattice points in certain polyhedra. Our main tool …
View article: The atomic Leibniz rule
The atomic Leibniz rule Open
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 operator associated to any atomic double coset. We prove t…
View article: On reduced expressions for core double cosets
On reduced expressions for core double cosets Open
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 combinatorial. One result of Elias-Ko is that any coset admits …
View article: Singular Light Leaves
Singular Light Leaves Open
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 between singular Soergel bimodules.
View article: On the size of Bruhat intervals
On the size of Bruhat intervals Open
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 computer calculations for these groups have led us to believe th…
View article: Subexpressions and the Bruhat order for double cosets
Subexpressions and the Bruhat order for double cosets Open
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 double cosets. This establishes the compatibility of the Bruh…
View article: Demazure operators for double cosets
Demazure operators for double cosets Open
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 we call the nilCoxeter category, and we also present this c…
View article: Combinatorial Invariance Conjecture for $\widetilde {A}_2$
Combinatorial Invariance Conjecture for $\widetilde {A}_2$ Open
The combinatorial invariance conjecture (due independently to Lusztig and Dyer) predicts that if $[x,y]$ and $[x^{\prime},y^{\prime}]$ are isomorphic Bruhat posets (of possibly different Coxeter systems), then the corresponding Kazhdan–Lus…
View article: Pre-canonical bases on affine Hecke algebras
Pre-canonical bases on affine Hecke algebras Open
For any affine Weyl group, we introduce the pre-canonical bases. They are a set of bases $\{\mathbf{N}^i\}_{1\leq i \leq m+1} $ (where $m$ is the height of the highest root) of the spherical Hecke algebra that interpolates between the stan…
View article: On the affine Hecke category for $SL_3$
On the affine Hecke category for $SL_3$ Open
We study the diagrammatic Hecke category associated with the affine Weyl group of type $\tilde{A}_2$. More precisely we find a (surprisingly simple) basis for the Hom spaces between indecomposable objects, that we call indecomposable doubl…
View article: On the affine Hecke category
On the affine Hecke category Open
We give a complete (and surprisingly simple) description of the affine Hecke category for $\tilde{A}_2$ in characteristic zero. More precisely, we calculate the Kazhdan-Lusztig polynomials, give a recursive formula for the projectors defin…
View article: p-Jones-Wenzl idempotents
p-Jones-Wenzl idempotents Open
For a prime number p and any natural number n we introduce, by giving an explicit recursive formula, the p-Jones-Wenzl projector JWnp, an element of the Temperley-Lieb algebra TLn(2) with coefficients in Fp. We prove that these projectors …
View article: The anti-spherical category
The anti-spherical category Open
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-Lusztig polynomials have non-negative coefficients, and that a m…
View article: A non-perverse Soergel bimodule in type <i>A</i>
A non-perverse Soergel bimodule in type <i>A</i> Open
A basic question concerning indecomposable Soergel bimodules is to understand their en-domorphism rings. In characteristic zero all degree-zero endomorphisms are isomorphisms (afact proved by Elias and the second author) which implies the …
View article: Indecomposable Soergel bimodules for universal Coxeter groups
Indecomposable Soergel bimodules for universal Coxeter groups Open
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 primes for which the positive characteristic analogue of S…
View article: Light leaves and Lusztig's conjecture
Light leaves and Lusztig's conjecture Open
We define a map F with domain a certain subset of the set of light leaves (certain morphisms between Soergel bimodules introduced by the author in an earlier paper) and range the set of prime numbers. Using results of Soergel we prove the …