Related papers: A trace formula for Hecke operators on Fuchsian gr…

We develop an explicit theory of formal modular forms over arbitrary number fields $K$, as functions of modular points. We define modular points for $\Gamma_0({\mathfrak n})$ and $\Gamma_1({\mathfrak n})$, where the level ${\mathfrak n}$ is…

We study Soergel modules for arbitrary Coxeter groups. For infinite Coxeter groups, we show that the homomorphisms between Soergel modules are in general more than those coming from morphisms of Soergel bimodules. This result provides a…

Let $N>1$ be an integer, and let $\Gamma = \Gamma_0 (N) \subset \SL_4 (\Z)$ be the subgroup of matrices with bottom row congruent to $(0,0,0,*)\mod N$. We compute $H^5 (\Gamma; \C) $ for a range of $N$, and compute the action of some Hecke…

In this paper, we review the construction of the Dirac operator for graded affine Hecke algebras and calculate the Dirac cohomology of irreducible unitary modules for the graded Hecke algebra of gl(n).

We construct a symmetric spectrum representing the G-equivariant K-theory of C*-algebras for a compact group or a proper groupoid G. Our spectrum is functorial for equivariant *-homomorphisms. We use this to establish the additivity of the…

For any formal group law, there is a formal affine Hecke algebra defined by Hoffnung, Malag\'on-L\'opez, Savage, and Zainoulline. Coming from this formal group law, there is also an oriented cohomology theory. We identify the formal affine…

Let ${\mathcal E}$ be a holomorphic vector bundle on a complex manifold $X$ such that $\dim_{{\mathbb C}}X=n$. Given any continuous, basic Hochschild $2n$-cocycle $\psi_{2n}$ of the algebra ${\rm Diff}_n$ of formal holomorphic differential…

We generalize the notion of trace to the Kontsevich quantization algebra and show that for all Poisson manifolds representable by quotients of a symplectic manifold by a Hamiltonian action of a nilpotent Lie group, the trace is given by…

Given a one-dimensional formal group of height 2, let E be the Morava E-theory spectrum associated to its universal deformation over the Lubin-Tate ring. By computing with moduli spaces of elliptic curves, we give an explicitation for an…

We construct a functor from the Hecke category to a groupoid built from the underlying Coxeter group. This fixes a gap in an earlier work of the authors. This functor provides an abstract realization of the localization of the Hecke…

In this paper, we introduce the cohomology theory of $\mathcal{O}$-operators on Hom-associative algebras. This cohomology can also be viewed as the Hochschild cohomology of a certain Hom-associative algebra with coefficients in a suitable…

In this paper we study a class of Jacobi operators, such that each operator is generated by the unit Borel measure with a support consisting of a finite number of intervals on the real line R and a finite number of points in C, located…

We present some results concerning the relative modular operator in semifinite von Neumann algebras. These results allow one to prove some basic formula for trace, to obtain equivalence between Araki's relative entropy and Umegaki's…

In this article we provide a framework for the study of Hecke operators acting on the Bredon (co)homology of an arithmetic discrete group. Our main interest lies in the study of Hecke operators for Bianchi groups. Using the Baum-Connes…

Motivated by recent advances in Catalan combinatorics, we study special values of the standard trace on affine Hecke algebras. Starting from a generating function for this trace calculated by Opdam, we use the theory of Szenes and Vergne to…

This paper outlines a covariant theory of operators defined on groups and homogeneous spaces. A systematic use of groups and their representations allows to obtain results of algebraic and analytical nature. The consideration is…

We study the quadratic residue weight enumerators of the dual projective Reed-Solomon codes of dimensions $5$ and $q-4$ over the finite field $\mathbb{F}_q$. Our main results are formulas for the coefficients of the the quadratic residue…

This article generalizes Venkatesh's structure theorem for the derived Hecke action on the Hecke trivial cohomology of a division algebra over an imaginary quadratic field to division algebras over all number fields. In particular, we show…

In this paper we define B-Fredholm elements in a Banach algebra $A$ modulo an ideal $J$ of $A.$ When a trace function is given on the ideal $J,$ it generate an index for B-Fredholm elements. In the case of a B-Fredholm operator $T$ acting…

An operator $H=H_{0}+V$ where $H_{0}=i^{-N} \partial^{N}$ ($N$ is arbitrary) and $V$ is a differential operator of order $N-1$ with coefficients decaying sufficiently rapidly at infinity is considered in the space $L^2(\Bbb R)$. The goal of…