We use pseudodeformation theory to study Mazur’s Eisenstein ideal. Given prime numbers N and p > 3, we study the Eisenstein part of the p-adic Hecke algebra for Γ0(N). We compute the rank of this Hecke algebra in terms of Massey products in Galois cohomology, answering a question of Mazur and generalizing a result of Calegari-Emerton. We also also give new proofs of Merel’s result on this rank ...

The goal of this paper is to define a new class of objects which we call triple groups and to relate them with Cherednik’s double affine Hecke algebras. This has as immediate consequences new descriptions of double affine Weyl and Artin groups, the double affine Hecke algebras as well as the corresponding elliptic objects. From the new descriptions we recover results of Cherednik on automorphis...

We investigate certain bases of Hecke algebras deened by means of the Yang-Baxter equation, which we call Yang-Baxter bases. These bases are essentially self-adjoint with respect to a canonical bilinear form. In the case of the degenerate Hecke algebra, we identify the coeecients in the expansion of the Yang-Baxter basis on the usual basis of the algebra with specializations of double Schubert ...

In this paper we introduce a new subspace of Jacobi forms of higher degree via certain relations among Fourier coefficients. We prove that this space can also be characterized by duality properties of certain distinguished embedded Hecke operators. We then show that this space is Hecke invariant with respect to all good Hecke operators. As explicit examples we give Eisenstein series. Conversely...

The goal of this paper is to define a new class of objects which we call triple affine Artin groups and to relate them with Cherednik’s double affine Hecke algebras. This has as immediate consequences new and simple descriptions of double affine Weyl and Artin groups, the double affine Hecke algebras as well as the corresponding elliptic objects. We also recover in an transparent and elementary...

We give a complete description of the category of smooth complex representations of the multiplicative group of a central simple algebra over a locally compact nonarchimedean local eld. More precisely, for each inertial class in the Bernstein spectrum, we construct a type and compute its Hecke algebra. The Hecke algebras that arise are all naturally isomorphic to products of a ne Hecke algebras...

We investigate certain bases of Hecke algebras defined by means of the YangBaxter equation, which we call Yang-Baxter bases. These bases are essentially selfadjoint with respect to a canonical bilinear form. In the case of the degenerate Hecke algebra, we identify the coefficients in the expansion of the Yang-Baxter basis on the usual basis of the algebra with specializations of double Schubert...

A Jesús Muñoz Díaz por su cumpleaños Contents 1. Introduction. 1 2. Elliptic sheaves and Hecke correspondences. Euler products 3 2.1. Elliptic sheaves 3 2.2. ∞-Level structures 5 2.3. Hecke correspondences 6 2.4. Euler products 8 3. Isogenies and Hecke correspondences 9 3.1. Isogenies for elliptic sheaves 9 3.2. Trivial correspondences 11 4. Ideal class group anhilators for the cyclotomic funct...

Let X be an arithmetic hyperbolic surface arising from a quaternion division algebra over Q. Let be a Hecke–Maass form on X , and let ` be a geodesic segment. We obtain a power saving over the local bound of Burq, Gérard, and Tzvetkov for the L-norm of restricted to `, by extending the technique of arithmetic amplification developed by Iwaniec and Sarnak. We also improve the local bounds for va...

In the past few years,much attention has been devoted to the behavior of eigenfunctions of classically chaotic quantum systems. One aspect of this topic concerns their value distribution and specifically their extreme values (see [Be], [AS], [S1], [IS], [HeR], [ABST]). Our aim is to explore this topic for one of the best-studied models in quantum chaotic dynamics—the quantized cat map (see [HB]...