Related papers: Bianchi period polynomials: Hecke action and congr…

We prove that every orthogonal Gelfand-Zeitlin algebra $U$ acts on its Gelfand-Zeitlin subalgebra $\Gamma$. Considering the dual module, we show that every Gelfand-Zeitlin character of $\Gamma$ is realizable in a $U$-module. We observe that…

In this paper, we construct a categorical double quantum Heisenberg action on the representation category of finite classical groups $\mathrm{O}_{2n+1}(q)$, $\mathrm{Sp}_{2n}(q)$ and $\mathrm{O}^{\pm}_{2n}(q)$ with $q$ odd. Over a field of…

Let $T_m(N,2k)$ denote the $m$-th Hecke operator on the space $S_{2k}(\Gamma_0(N))$ of cuspidal modular forms of weight $2k$ and level $N$. In this paper, we study the non-repetition of the second coefficient of the characteristic…

Let $\Lambda$ and $\Gamma$ be artin algebras and $_{\Lambda}U_{\Gamma}$ a faithfully balanced selforthogonal bimodule. In this paper, we first introduce the notion of $k$-Gorenstein modules with respect to $_{\Lambda}U_{\Gamma}$ and then…

In this paper an explicit formula is given for a sequence of numbers. The positivity of this sequence of numbers implies that zeros in the critical strip of the Euler product of Hecke polynomials, which are associated with the space of cusp…

Suppose $\Gamma$ is an arithmetic group defined over a global field $K$, that the $K$-type of $\Gamma$ is $A_n$ with $n \geq 2$, and that the ambient semisimple group that contains $\Gamma$ as a lattice has at least two noncocompact…

In this text, we develop the theory of vectorial modular forms with values in Tate algebras introduced by the first author, in a very special case (dimension two, for a very particular representation of {\Gamma} := GL 2 (Fq[$theta$])).…

We consider the problem of defining an action of Hecke operators on the coherent cohomology of certain integral models of Shimura varieties. We formulate a general conjecture describing which Hecke operators should act integrally and solve…

The structure of orthogonal polynomials on $\mathbb{R}^{2}$ with the weight function $| x_{1}^{2}-x_{2}^{2}|^{2k_{0}}| x_{1}x_{2}|^{2k_{1}}e^{-(x_{1}^{2}+x_{2}^{2})/2}$ is based on the Dunkl operators of type $B_{2}$. This refers to the…

Bianchi modular forms are automorphic forms over an imaginary quadratic field, associated to a Bianchi group. Even though modern studies of Bianchi modular forms go back to the mid 1960's, most of the fundamental problems surrounding their…

Let $G$ be a split reductive group over a finite field $k$. In this note we study the space $V$ of finitely supported functions on the set of isomorphism classes $G$-bundles on the projective line ${\mathbb P}^1$ endowed with a…

A loop quantization of the diagonal class A Bianchi models starting from the complex-valued self-dual connection variables is presented in this paper. The basic operators in the quantum theory correspond to areas and generalized holonomies…

Let $p$ be a prime and let $S_2(\Gamma(p))$ be the space of weight $2$ cusp forms for the principal congruence subgroup $\Gamma(p)$. Then $\mathrm{SL}_2(\mathbb{F}_p)$ acts on $S_2(\Gamma(p))$ in a natural way. Around 1928, Hecke proved…

For a compact real form $U$ of a complex simple Lie group $G$, and an irreducible representation $\rho:\Gamma \to U$ of a Fuchsian group of the first kind $\Gamma$, it is shown that the classical isomorphism of Shimura, for the periods of a…

We prove that if a countable group $\Gamma$ contains infinite commuting subgroups $H, H'\subset \Gamma$ with $H$ non-amenable and $H'$ ``weakly normal'' in $\Gamma$, then any measure preserving $\Gamma$-action on a probability space which…

We consider the moduli space ${\cal M}(G)$ of $G$-Higgs bundles over a compact Riemann surface $X$, where $G$ is a semisimple complex Lie group, and study the action of a finite group $\Gamma$ on ${\cal M}(G)$ induced by a holomorphic…

An extension of the Lorentz group that includes generators $\Gamma^\mu$ carrying a space-time index has been previously demonstrated to \emph{explicitly} construct the Minkowski metric \emph{within} the internal group space as a consequence…

We define the degenerate two boundary affine Hecke-Clifford algebra $\mathcal{H}_d$, and show it admits a well-defined $\mathfrak{q}(n)$-linear action on the tensor space $M\otimes N\otimes V^{\otimes d}$, where $V$ is the natural module…

Let $k\geq 2$ and $n\geq 1$ be any integers. In this paper, we prove that all Hecke operators act trivially on the space of ordinary Drinfeld cuspforms of level $\Gamma_1(t^n)$ and weight $k$.

We study a relationship between $Q$-polynomial distance-regular graphs and the double affine Hecke algebra of type $(C^{\vee}_1,C_1)$. Let $\Gamma$ denote a $Q$-polynomial distance-regular graph with vertex set $X$. We assume that $\Gamma$…