4 citations · 10 across the 16 of their papers we have counts for
17 papers
Categorical representations of algebraic groups in positive characteristic
Pramod N. Achar, Gurbir Dhillon, Simon Riche
In this paper we present a formalism of categorical representation theory for affine group schemes of finite type over fields (both in the weak and strong settings) which applies t…
Equivariant Koszul Duality, Modular Category , and Periodic Kazhdan--Lusztig Polynomials
Simon Riche, Quan Situ
Let be a connected reductive algebraic group over an algebraically closed field of positive characteristic, be its Lie algebra, and be a Borel subgroup. We p…
Tilting modules for reductive algebraic groups: characters and support varieties
Pramod N. Achar, Simon Riche
These notes are our contribution to the Proceedings of the ICM 2026. We discuss some results we have obtained (in part jointly with coauthors) regarding the representation theory o…
Modular intersection cohomology of Drinfeld's compactifications
Pramod N. Achar, Gurbir Dhillon, Simon Riche
We compute the dimension of the cohomology of stalks of intersection cohomology complexes on Zastava schemes and Drinfeld compactifications associated with a connected reductive al…
On the modular generalized Springer correspondence for disconnected groups
Kostas I. Psaromiligkos, Simon Riche
We study the construction of a modular generalized Springer correspondence for a possibly disconnected complex reductive algebraic group.
Semiinfinite sheaves on affine flag varieties
Pramod N. Achar, Gurbir Dhillon, Simon Riche
We study a category of semiinfinite sheaves on the affine flag variety of a connected reductive algebraic group, with coefficients in a field (of arbitrary characteristic different…
Mixed modular perverse sheaves on affine flag varieties and Koszul duality
Simon Riche
Under some technical assumptions, and building on joint work with Bezrukavnikov, we prove a multiplicity formula for indecomposable tilting perverse sheaves on affine flag varietie…
A modular ramified geometric Satake equivalence
Pramod N. Achar, João Lourenço, Timo Richarz +1
We extend the ramified geometric Satake equivalence due to Zhu (for tamely ramified groups) and the third named author (in full generality) from rational coefficients to include mo…
Some applications of the geometric Satake equivalence to modular representation theory
Simon Riche
These notes present an application of the geometric Satake equivalence to the description of characters of indecomposable tilting modules for reductive algebraic groups over fields…
On two modular geometric realizations of an affine Hecke algebra
Roman Bezrukavnikov, Simon Riche
In this paper we construct equivalences of monoidal categories relating three geometric or representation-theoretic categorical incarnations of the affine Hecke algebra of a connec…
Higher nearby cycles and central sheaves on affine flag varieties
Pramod N. Achar, Simon Riche
In this paper we generalize and study a notion of (unipotent) nearby cycles over a higher dimensional base based on Beĭlinson's description of unipotent nearby cycles, following an…
Koszul duality for Coxeter groups
Simon Riche, Cristian Vay
We construct a "Koszul duality" equivalence relating the (diagrammatic) Hecke category attached to a Coxeter system and a given realization to the Hecke category attached to the sa…
Fixed points under pinning-preserving automorphisms of reductive group schemes
Pramod N. Achar, João Lourenço, Timo Richarz +1
In this paper we determine the scheme-theoretic fixed points of pinned reductive group schemes acted upon by a group of pinning-preserving automorphisms. The results are used in a…
Modular affine Hecke category and regular centralizer
Roman Bezrukavnikov, Simon Riche
In this paper we provide a "combinatorial" description of the category of tilting perverse sheaves on the affine flag variety of a reductive algebraic group, and its free-monodromi…
A geometric model for blocks of Frobenius kernels
Pramod N. Achar, Simon Riche
Building on a geometric counterpart of Steinberg's tensor product formula for simple representations of a connected reductive algebraic group over a field of positive character…
Modular affine Hecke category and regular unipotent centralizer
R. Bezrukavnikov, S. Riche, L. Rider
In this paper we provide, under some mild explicit assumptions, a geometric description of the category of representations of the centralizer of a regular unipotent element in a re…
Representation theory of disconnected reductive groups
P. Achar, W. Hardesty, S. Riche
We study three fundamental topics in the representation theory of disconnected algebraic groups whose identity component is reductive: (i) the classification of irreducible represe…