94 citations · 407 across the 32 of their papers we have counts for
29 papers · 1 filter
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 Hecke category is bigraded
Ben Elias
The Hecke category is bigraded. For completeness, we classify gradings on the Hecke category. We also classify object-preserving autoequivalences.
Categorical diagonalization and -cells
Ben Elias, Lars Thorge Jensen, Joel Gibson
In the Iwahori-Hecke algebra, the full twist acts on cell modules by a scalar, and the half twist acts by a scalar and an involution. A categorification of this statement, describi…
A singular Coxeter presentation
Ben Elias, Hankyung Ko
We enlarge a Coxeter group into a category, with one object for each finite parabolic subgroup, encoding the combinatorics of double cosets. This category, the singular Coxeter mon…
Type Webs
Elijah Bodish, Ben Elias, David E. V. Rose +1
We define a -linear pivotal category and prove that it is equivalent to the full subcategory of finite-dimensional representations…
Actions of sl_2 on algebras appearing in categorification
Ben Elias, You Qi
We prove that many of the recently-constructed algebras and categories which appear in categorification can be equipped with an action of by derivations. The $\ma…
Localized calculus for the Hecke category
Ben Elias, Geordie Williamson
We construct a functor from the Hecke category to a groupoid built from the underlying Coxeter group. This fixes a gap in an earlier work of the authors. This functor provides an a…
Categorifying Hecke algebras at prime roots of unity, part I
Ben Elias, You Qi
We equip the type diagrammatic Hecke category with a special derivation, so that after specialization to characteristic it becomes a -dg category. We prove that the defi…
A diamond lemma for Hecke-type algebras
Ben Elias
In this paper we give a version of Bergman's diamond lemma which applies to certain monoidal categories presented by generators and relations. In particular, it applies to: the Cox…
Gaitsgory's central sheaves via the diagrammatic Hecke category
Ben Elias
We initiate the study of Gaitsgory's central sheaves using complexes of Soergel bimodules, in extended affine type A. We conjecture that the complex associated to the standard repr…
Categorical diagonalization of full twists
Ben Elias, Matthew Hogancamp
We conjecture that the complex of Soergel bimodules associated with the full twist braid is categorically diagonalizable, for any finite Coxeter group. This utilizes the theory of…
Categorical diagonalization
Ben Elias, Matthew Hogancamp
This paper lays the groundwork for the theory of categorical diagonalization. Given a diagonalizable operator, tools in linear algebra (such as Lagrange interpolation) allow one to…
Modular representation theory in type A via Soergel bimodules
Ben Elias, Ivan Losev
In this paper we express certain multiplicities in modular representation-theoretic categories of type A in terms of affine p-Kazhdan-Lusztig polynomials. The representation-theore…
Relative hard Lefschetz for Soergel bimodules
Ben Elias, Geordie Williamson
We prove the relative hard Lefschetz theorem for Soergel bimodules. It follows that the structure constants of the Kazhdan-Lusztig basis are unimodal. We explain why the relative h…
Folding with Soergel bimodules
Ben Elias
We give a gentle introduction to the concept of folding. That is, we provide an elementary discussion of equivariant categories, their weighted Grothendieck groups, and the technic…
Light ladders and clasp conjectures
Ben Elias
Morphisms between tensor products of fundamental representations of the quantum group of sl(n) are described by the sl(n)-webs of Cautis-Kamnitzer-Morrison. Using these webs, we pr…
Trace decategorification of the Hecke category
Ben Elias, Aaron D. Lauda
We compute the trace decategorification of the Hecke category for an arbitrary Coxeter group. More generally, we introduce the notion of a strictly object-adapted cellular category…
A categorification of quantum sl(2) at prime roots of unity
Ben Elias, You Qi
We categorify the Beilinson-Lusztig-MacPherson integral form of quantum sl(2) specialized at a prime root of unity.
Diagrammatics for Coxeter groups and their braid groups
Ben Elias, Geordie Williamson
We give a monoidal presentation of Coxeter and braid 2-groups, in terms of decorated planar graphs. This presentation extends the Coxeter presentation. We deduce a simple criterion…
Quantum Satake in type A: part I
Ben Elias
We give an interpretation of sl_n webs as morphisms between certain singular Soergel bimodules. We explain how this is a combinatorial, algebraic version of the geometric Satake eq…
Kazhdan-Lusztig conjectures and shadows of Hodge theory
Ben Elias, Geordie Williamson
We give an informal introduction to the authors' work on some conjectures of Kazhdan and Lusztig, building on work of Soergel and de Cataldo-Migliorini. This article is an expanded…
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…
The two-color Soergel calculus
Ben Elias
We give a diagrammatic presentation for the category of Soergel bimodules for the dihedral group W . The (two-colored) Temperley-Lieb category is embedded inside this category as t…
On cubes of Frobenius extensions
Ben Elias, Noah Snyder, Geordie Williamson
Given a hypercube of Frobenius extensions between commutative algebras, we provide a diagrammatic description of some natural transformations between compositions of induction and…