Related papers: Algebres de Hecke affines generiques

We study the structure of the Eisenstein component of Hida's ordinary p-adic Hecke algebra attached to modular forms, in connection with the companion forms in the space of modular forms (mod p). We show that such an algebra is a Gorenstein…

Let G be an orthogonal or symplectic p-adic group (not necessarily split) or an inner form of a general linear p-adic group. In a previous paper, it was shown that the Bernstein components of the category of smooth representations of G are…

We use Bernstein's presentation of the Iwahori-Matsumoto Hecke algebra to obtain a simple proof of the Satake isomorphism and, in the same stroke, compute the center of the Iwahori-Matsumoto Hecke algebra.

Let $U(p)$ denote the Atkin operator of prime index $p$. Honda and Kaneko proved infinite families of congruences of the form $f|U(p) \equiv 0 \pmod{p}$ for weakly holomorphic modular forms of low weight and level and primes $p$ in certain…

We study the growth of representations of the Lie algebra of vector fields on the affine space that admit a compatible action of the polynomial algebra. We establish the Bernstein inequality for these representations, enabling us to focus…

Assume that $\mathbb F$ is an algebraically closed field and let $q$ denote a nonzero scalar in $\mathbb F$ that is not a root of unity. The universal DAHA (double affine Hecke algebra) $\mathfrak H_q$ of type $(C_1^\vee,C_1)$ is a unital…

Let ${\mathfrak o}$ be the ring of integers in a finite extension $K$ of ${\mathbb Q}_p$, let $k$ be its residue field. Let $G$ be a split reductive group over ${\mathbb Q}_p$, let $T$ be a maximal split torus in $G$. Let ${\mathcal…

We introduce and study some affine Hecke algebras of type ADE, generalising the affine Hecke algebras of GL. We construct irreducible calibrated representations and describe the calibrated spectrum. This is done in terms of new families of…

The central result of this paper is a refinement of Hida's duality theorem between ordinary Lambda-adic modular forms and the universal ordinary Hecke algebra. Specifically, we give a necessary condition for this duality to be integral with…

We apply the crystal basis theory for Fock spaces over quantum affine algebras to the modular representations of the cyclotomic Hecke algebras of type $G(p,p,n)$. This yields a classification of simple modules over these cyclotomic Hecke…

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…

We show that graded Hecke algebras are PI algebras if and only if they are finitely generated over their centres if and only if the deformation parameters $t_{i}$ are zero for all $i=1,\ldots,N$. This generalises a result for symplectic…

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…

In this paper we construct equivalences of monoidal categories relating three geometric or representation-theoretic categorical incarnations of the affine Hecke algebra of a connected reductive algebraic group $G$ over a field of positive…

We start the general structure theory of not necessarily semisimple finite tensor categories, generalizing the results in the semisimple case (i.e. for fusion categories), obtained recently in our joint work with D.Nikshych. In particular,…

In this doctoral thesis, we will determine the image of Artin groups associated to all finite irreducible Coxeter groups inside their associated finite Iwahori-Hecke algebra. This was done in type $A$ by Brunat, Magaard and Marin. The…

Let $G$ be a split reductive $p$-adic group. Let ${\mathcal H}(G)$ be its Hecke algebra and let ${\mathcal C}(G)\supset {\mathcal H}(G)$ be the Harish-Chandra Schwartz algebra. The purpose of this note is to give a spectral interpretation…

We study a two-boundary extension of the Temperley-Lieb algebra which has recently arisen in statistical mechanics. This algebra lies in a quotient of the affine Hecke algebra of type C and has a natural diagrammatic representation. The…

Consider the affine Hecke algebra $H_l$ corresponding to the group $GL_l$ over a $p$-adic field with the residue field of cardinality $q$. Regard $H_l$ as an associative algebra over the field $C(q)$. Consider the $H_{l+m}$-module $W$…

Every double coset in $\text{GL}_m(k[[z]])\backslash \text{GL}_m(k((z)))/\text{GL}_m(k((z^2)))$ is uniquely represented by a block diagonal matrix with diagonal blocks in $\{1,z, \begin{pmatrix} 1& z\\ 0 &z^i \end{pmatrix} (i>1)\}$ if…