Related papers: Computing Hecke eigenvalues below the cohomologica…

We propose a method for calculating cohomology operations for finite simplicial complexes. Of course, there exist well--known methods for computing (co)homology groups, for example, the reduction algorithm consisting in reducing the…

Let Q be an affine semigroup generating Z^d, and fix a finitely generated Z^d-graded module M over the semigroup algebra k[Q] for a field k. We provide an algorithm to compute a minimal Z^d-graded injective resolution of M up to any desired…

Let $p\geq 5$ be a prime number, $G$ a split connected reductive group defined over a $p$-adic field, and $I_1$ a choice of pro-$p$-Iwahori subgroup. Let $C$ be an algebraically closed field of characteristic $p$ and $\mathcal{H}$ the…

We propose a method for reduction of quantum systems with arbitrary first class constraints. An appropriate mathematical setting for the problem is homology of associative algebras. For every such an algebra $A$ and its subalgebra B with an…

Let K be an imaginary quadratic field with class number one and ring of integers O. We prove that mod l, a system of Hecke eigenvalues occurring in the first cohomology group of some congruence subgroup Gamma of SL(2,O) can be realized in…

We apply discrete algebraic Morse theory to calculate the Anick resolution of the group algebra of the group $G_3^2$. As a corollary, we evaluate Hochschild cohomologies of $G_3^2$ with coefficients in all 1-dimensional bimodules. Almost…

Recently Delorme and Opdam have generalized the theory of R-groups towards affine Hecke algebras with unequal labels. We apply their results in the case where the affine Hecke algebra is of type B, for an induced discrete series…

We study Hecke operators on moduli spaces of ramified $G$-bundles using the combinatorial language of Hecke graphs. We introduce a general notion of $\mathcal H$-ramification in the spirit of parahoric ramification, which depends on a…

We construct a basis for the space of half-integral weight Siegel Eisenstein series of level 4N where N is odd and square-free. Then we restrict our attention to those Eisenstein series generated from elements of $\Gamma_0(4)$, commenting…

The main objective of this paper is to compute $RO(G)$-graded cohomology of $G$-orbits for the group $G=C_n$, where $n$ is a product of distinct primes. We compute these groups for the constant Mackey functor $\underline{Z}$ and for the…

We compute the sheaf cohomology with constant $\mathbb{Z}_2$ coefficients of a concrete class of locally profinite sets of independent interest. We introduce $k$-sheer partitions to aid in constructions. It is also shown that questions of…

We develop cohomological interpretations for several types of automorphic forms for Hecke triangle groups of infinite covolume. We then use these interpretations to establish explicit isomorphisms between spaces of automorphic forms,…

In this paper, we consider Hecke triangle groups $\Gamma_w$ for $w>2$ and associated infinite-volume orbifolds $\Gamma_w \backslash \mathbb{H}$. We show that the Selberg zeta function $Z_{\Gamma_w}(s)$ can be approximated for $s \in…

This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. For a two-dimensional local field a Hecke algebra which is formed by operators which integrate…

Given a reductive group G, Kostant and Kumar defined a nil Hecke algebra that may be viewed as a degenerate version of the double affine nil Hecke algebra introduced by Cherednik. In this paper, we construct an isomorphism of the spherical…

Let E_lambda be the Hilbert space spanned by the eigenfunctions of the non-Euclidean Laplacian associated with a positive discrete eigenvalue lambda. In this paper, the trace of Hecke operators T_n acting on the space E_lambda is computed…

For $k\ge 2$ even, let $d_{k,N}$ denote the dimension of the largest simple Hecke submodule of $S_{k}(\Gamma_0(N); \mathbb{Q})^\text{new}$. We show, using a simple analytic method, that $d_{k,N} \gg_k \log\log N / \log(2p)$ with $p$ the…

We consider the eigenvalue equation for the Laplace-Beltrami operator acting on scalar functions on the non-compact Eguchi-Hanson space. The corresponding differential equation is reducible to a confluent Heun equation with Ince symbol…

We show that the systems of Hecke eigenvalues that appear in the coherent cohomology with coefficients in automorphic line bundles of any mod $p$ abelian type compact Shimura variety at hyperspecial level are the same as those appearing in…

We study sums of absolute values of Hecke eigenvalues of $\textrm{GL}(2)$ representations that are tempered at all finite places. We show that these sums exhibit logarithmic savings over the trivial bound if and only if the representation…