Related papers: The Hecke Bicategory

We classify the finite dimensional irreducible representations of affine Hecke algebras of type B_2 with unequal parameters.

We generalize graded Hecke algebras to include a twisting two-cocycle for the associated finite group. We give examples where the parameter spaces of the resulting twisted graded Hecke algebras are larger than that of the graded Hecke…

The endomorphism algebras of the permutation modules for transitive permutation groups, known as Hecke algebras, are fundamental objects in representation theory. While group algebras are known to be symmetric over any field, it is natural…

The representation theory of 0-Hecke-Clifford algebras as a degenerate case is not semisimple and also with rich combinatorial meaning. Bergeron et al. have proved that the Grothendieck ring of the category of finitely generated…

This paper surveys, and in some cases generalises, many of the recent results on homomorphisms and the higher Ext groups for q-Schur algebras and for the Hecke algebra of type A. We review various results giving isomorphisms between Ext…

We study the subgroup structure, Hecke algebras, quasi-regular representations, and asymptotic properties of some fractal groups of branch type. We introduce parabolic subgroups, show that they are weakly maximal, and that the corresponding…

Let $G$ be a finite group, $H \le G$ a subgroup, $R$ a commutative ring, $A$ an $R$-algebra, and $\alpha$ an action of $G$ on $A$ by $R$-algebra automorphisms. We study the associated \emph{skew Hecke algebra}…

Aiming for a revival of the theory of crystallographic complex reflection groups, we compute (minimal) Coxeter-like reflection presentations for the infinite families of those non-genuine groups which satisfy Steinberg's fixed point…

This paper introduces the notion of calibrated representations for affine Hecke algebras and classifies and constructs all finite dimensional irreducible calibrated representations. The main results are that (1) irreducible calibrated…

The main result of this paper shows that, over large enough fields of characteristic different from $2$, the alternating Hecke algebras are $\mathbb{Z}$-graded algebras that are isomorphic to fixed-point subalgebras of the quiver Hecke…

In this work, we study multiplicity-free induced representations of finite groups. We analyze in great detail the structure of the Hecke algebra corresponding to the commutant of an induced representation and then specialize to the…

In the paper, we give an explicit basis of the cyclotomic quiver Hecke algebra corresponding to a minuscule representation of finite type.

We consider a 2-dimensional representation of the Hecke algebra $\mathcal{H}(G_7, u)$, where $G_7$ is the complex reflection group and $u$ is the set of indeterminates $u=(x_1, x_2, y_1, y_2, y_3, z_1, z_2, z_3)$. After specializing the…

We construct a diagrammatic categorification of the spherical module over the Hecke algebra. We establish a basis for the morphism spaces of this category, and prove that it is equivalent to an existing algebraic spherical category.

Let $G$ be a direct product of inner forms of general linear groups over non-archimedean locally compact fields of residue characteristic $p$ and let $K^1$ be the pro-$p$-radical of a maximal compact open subgroup of $G$. In this paper we…

Ideas from Hodge theory have found important applications in representation theory. We give a survey of joint work with Ben Elias which uncovers Hodge theoretic structure in the Hecke category ("Soergel bimodules"). We also outline…

In this paper we outline the Hecke theory for Hermitian modular forms in the sense of Hel Braun for arbitrary class number of the attached imaginary-quadratic number field. The Hecke algebra turns out to be commutative. Its inert part has a…

The paper constructs new Hecke endomorphism algebras with a stratified structure. A novel feature of the proof is to approach difficult Ext^1 vanishing conditions by building entire exact category structures in which the analogous vanishing…

We introduce extensions of the multidimensional Heisenberg group $\mathbb{H}^n$ by two-parameter groups of dilations, and then classify the extended groups up to isomorphism, by employing Lie algebra techniques. We show that the groups are…

We consider the analog of Gelfand-Graev representations of the uniteriangular group. We obtain the decomposition into the sum of irreducible representations, prove that these representations are multiplicity free, calculate the Hecke…