Related papers: The Hecke algebra of a Frobenius P-category

In "Frobenius Categories versus Brauer Blocks", Progress in Math. 274, we introduce the Frobenius P-categories giving two quite different definitions of them. In this paper, we exhibit a third equivalent definition based on the form of the…

We consider four classes of classical groups over a non-archimedean local field F: symplectic, (special) orthogonal, general (s)pin and unitary. These groups need not be quasi-split over F. The main goal of the paper is to obtain a local…

It is well-known that affine Hecke algebras are very useful to describe the smooth representations of any connected reductive p-adic group G, in terms of the supercuspidal representations of its Levi subgroups. The goal of this paper is to…

Using the results of J. Arthur on the representation theory of classical groups with additional work by Colette Moeglin and its relation with representations of affine Hecke algebras established by the author, we show that the category of…

We introduce a commutative associative graded algebra structure on the direct sum Z of the centers of the Hecke algebras associated to the symmetric groups in n letters for all n. As a natural deformation of the classical construction of…

We describe an algorithm for computing the $p$-canonical basis of the Hecke algebra, or one of its antispherical modules. The algorithm does not operate in the Hecke category directly, but rather uses a faithful embedding of the Hecke…

We further develop the abstract representation theory of affine Hecke algebras with arbitrary positive parameters. We establish analogues of several results that are known for reductive p-adic groups. These include: the relation between…

We associate a diagrammatic monoidal category $\mathcal{H}\textit{eis}_k(A;z,t)$, which we call the quantum Frobenius Heisenberg category, to a symmetric Frobenius superalgebra $A$, a central charge $k \in \mathbb{Z}$, and invertible…

We introduce the spin Hecke algebra, which is a q-deformation of the spin symmetric group algebra, and its affine generalization. We establish an algebra isomorphism which relates our spin (affine) Hecke algebras to the (affine)…

We establish a transfer of unitarity for a Bernstein component of the category of smooth representations of a reductive p-adic group to the associated Hecke algebra, in the framework of the theory of types, whenever the Hecke algebra is an…

We define a category of planar diagrams whose Grothendieck group contains an integral version of the infinite rank Heisenberg algebra, thus yielding a categorification of this algebra. Our category, which is a q-deformation of one defined…

Let $G$ be a reductive group over a non-archimedean local field $F$ of residue characteristic $p$. We prove that the Hecke algebras of $G(F)$ with coefficients in a ${\mathbb Z}_{\ell}$-algebra $R$ for $\ell$ not equal to $p$ are finitely…

We introduce a generalization of degenerate affine Hecke algebra, called wreath Hecke algebra, associated to an arbitrary finite group G. The simple modules of the wreath Hecke algebra and of its associated cyclotomic algebras are…

For a finite central extension $\tilde{G}$ of a classical $p$-adic reductive group, we consider the endomorphism algebra of some induced projective generator \`a la Bernstein of the category of smooth representations of $\tilde{G}$. In the…

Associated to the classical Weyl groups, we introduce the notion of degenerate spin affine Hecke algebras and affine Hecke-Clifford algebras. For these algebras, we establish the PBW properties, formulate the intertwiners, and describe the…

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…

Let F be a non-archimedean local field and let $G^\sharp$ be the group of F-rational points of an inner form of $SL_n$. We study Hecke algebras for all Bernstein components of $G^\sharp$, via restriction from an inner form G of $GL_n (F)$.…

Hecke algebras are usually defined algebraically, via generators and relations. We give a new algebro-geometric construction of affine and double-affine Hecke algebras (the former is known as the Iwahori-Hecke algebra, and the latter was…

We investigate the relative assembly map from the family of finite subgroups to the family of virtually cyclic subgroups for the algebraic $K$-theory of twisted group rings of a group G with coefficients in a regular ring R or, more…

We present an application of the program of groupoidification leading up to a sketch of a categorification of the Hecke algebroid --- the category of permutation representations of a finite group. As an immediate consequence, we obtain a…