相关论文: Hall algebras and graphs of Hecke operators for el…

We give a construction of an affine Hecke algebra associated to any Coxeter group acting on an abelian variety by reflections; in the case of an affine Weyl group, the result is an elliptic analogue of the usual double affine Hecke algebra.…

Let F be the cubic field of discriminant -23 and O its ring of integers. Let Gamma be the arithmetic group GL_2 (O), and for any ideal n subset O let Gamma_0 (n) be the congruence subgroup of level n. In a previous paper, two of us (PG and…

We continue to develop the analytic Langlands program for curves over local fields initiated in arXiv:1908.09677, arXiv:2103.01509 following a suggestion of Langlands and a work of Teschner. Namely, we study the Hecke operators introduced…

Let X be a smooth projective curve over a finite field. We describe H, the full Hall algebra of vector bundles X as a Feigin-Odesskii shuffle algebra. This shuffle algebra corresponds to the scheme S of all cusp eigenforms and to the…

Hecke operators acting on modular functions arise naturally in the context of 2d conformal field theory, but in seemingly disparate areas, including permutation orbifold theories, ensembles of code CFTs, and more recently in the context of…

In this article we describe the Hall algebra H_X of an elliptic curve X defined over a finite field and show that the group SL(2,Z) of exact auto-equivalences of the derived category D^b(Coh(X)) acts on the Drinfeld double DH_X of H_X by…

A diagram of algebras is a functor valued in a category of associative algebras. I construct an operad acting on the Hochschild bicomplex of a diagram of algebras. Using this operad, I give a direct proof that the Hochschild cohomology of a…

This paper investigates the connections between buildings and Hecke algebras through the combinatorial study of two algebras spanned by averaging operators on buildings. As a consequence we obtain a geometric and combinatorial description…

For a smooth quasi-projective surface S over complex numbers we consider the Borel-Moore homology of the stack of coherent sheaves on S with compact support and make this space into an associative algebra by a version of the Hall…

Let F be a real quadratic field with ring of integers O and with class number 1. Let Gamma be a congruence subgroup of GL_2 (O). We describe a technique to compute the action of the Hecke operators on the cohomology H^3 (Gamma; C). For F…

In this article, we investigate Hecke modifications of vector bundles on a smooth projective curve $X$ defined over an arbitrary field. We obtain structural results that allow us to reduce the classification problem of Hecke modifications…

We construct Hall algebra of elliptic curve over $\mathbb{F}_1$ using the theory of monoidal scheme due to Deitmar and the theory of Hall algebra for monoidal representations due to Szczesny. The resulting algebra is shown to be a…

This paper presents a comprehensive study of H-Toeplitz operators on the Fock space, a class of operators that synthesizes structural elements of both Toeplitz and Hankel operators. We derive explicit matrix representations for these…

We present some applications of ideas from partial differential equations and differential geometry to the study of difference equations on infinite graphs. All operators that we consider are examples of "elliptic operators" as defined by…

We study the action of Hecke operators on the set of hypergeometric functions. We show that the spectrum of these operators is the set of powers n^a and that polylogarithms play a dominant role in the study of the corresponding…

For $n\in\mathbb{N}$ and $\ell\in\{0,1,\dots,n\}$, we consider the function extracting the $\ell$th coefficient of the Ehrhart polynomials of lattice polytopes in $\mathbb{R}^n$. These functions form a basis of the space of unimodular…

We define graded hyper-algebras of vector-valued Siegel modular forms, which allow us to study tensor products of the latter. We also define vector-valued Hecke operators for Siegel modular forms at all places of ${\mathbb Q}$, acting on…

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…

We study Hecke algebras of groups acting on trees with respect to geometrically defined subgroups. In particular, we consider Hecke algebras of groups of automorphisms of locally finite trees with respect to vertex and edge stabilizers and…

We present a method to compute two Hecke operators acting on a space of algebraic modular forms simultaneously based on an idea of Eichler's. We show that in certain cases this method can be used to obtain the action of the full Hecke…