18 citations · 69 across the 15 of their papers we have counts for
13 papers · 1 filter
The center of the asymptotic Hecke category and unipotent character sheaves
Liam Rogel, Ulrich Thiel
In 2015, Lusztig [Bull. Inst. Math. Acad. Sin. (N.S.)10(2015), no.1, 1-72] showed that for a connected reductive group over an algebraic closure of a finite field the associated (g…
The Rank One property for free Frobenius extensions
Gwyn Bellamy, Ulrich Thiel
A conjecture by the second author, proven by Bonnafé-Rouquier, says that the multiplicity matrix for baby Verma modules over the restricted rational Cherednik algebra has rank one…
Wreath Macdonald polynomials at q=t as characters of rational Cherednik algebras
Dario Mathiä, Ulrich Thiel
Using the theory of Macdonald, Gordon showed that the graded characters of the simple modules for the restricted rational Cherednik algebra by Etingof and Ginzburg associated to th…
Cellularity of endomorphism algebras of tilting objects
Gwyn Bellamy, Ulrich Thiel
We show that, in a highest weight category with duality, the endomorphism algebra of a tilting object is naturally a cellular algebra. Our proof generalizes a recent construction o…
Cores of graded algebras with triangular decomposition
Gwyn Bellamy, Ulrich Thiel
We consider self-injective finite-dimensional graded algebras admitting a triangular decomposition. In a preceding paper, we have shown that the graded module category of such an a…
Highest weight theory for finite-dimensional graded algebras with triangular decomposition
Gwyn Bellamy, Ulrich Thiel
We show that the category of graded modules over a finite-dimensional graded algebra admitting a triangular decomposition can be endowed with the structure of a highest weight cate…
Hyperplane arrangements associated to symplectic quotient singularities
Gwyn Bellamy, Travis Schedler, Ulrich Thiel
We study the hyperplane arrangements associated, via the minimal model programme, to symplectic quotient singularities. We show that this hyperplane arrangement equals the arrangem…
Restricted rational Cherednik algebras
Ulrich Thiel
We give an overview of the representation theory of restricted rational Cherednik algebras. These are certain finite-dimensional quotients of rational Cherednik algebras at t=0. Th…
Blocks in flat families of finite-dimensional algebras
Ulrich Thiel
We study the behavior of blocks in flat families of finite-dimensional algebras. In a general setting we construct a finite directed graph encoding a stratification of the base sch…
Cuspidal Calogero-Moser and Lusztig families for Coxeter groups
Gwyn Bellamy, Ulrich Thiel
The goal of this paper is to compute the cuspidal Calogero-Moser families for all infinite families of finite Coxeter groups, at all parameters. We do this by first computing the s…
CHAMP: A Cherednik Algebra Magma Package
Ulrich Thiel
We present a computer algebra package based on Magma for performing computations in rational Cherednik algebras at arbitrary parameters and in Verma modules for restricted rational…
Decomposition matrices are generically trivial
Ulrich Thiel
We establish a genericity property in the representation theory of a flat family of finite-dimensional algebras in the sense of Cline-Parshal-Scott. More precisely, we show that th…
A counter-example to Martino's conjecture about generic Calogero-Moser families
Ulrich Thiel
The Calogero-Moser families are partitions of the irreducible characters of a complex reflection group derived from the block structure of the corresponding restricted rational Che…