Related papers: The Voronoi formula on GL(3) with ramification

By an automorphism of a topological group G we mean an isomorphism of G onto itself which is also a homeomorphism. In this article, we study the automorphism group Aut(G) of a dense subgroup G of R^n, n>=1. We show that Aut(G) can be…

Let $V$ be a simple vertex operator algebra which admits the continuous, faithful action of a compact Lie group $G$ of automorphisms. We establish a Schur-Weyl type duality between the unitary, irreducible modules for $G$ and the…

We utilize the structure of quasiautomorphic forms over an arbitrary Hecke triangle group to define a new vector analogue of an automorphic form. We supply a proof of the functional equations that hold for these functions modulo the group…

From a spectral identity we obtain asymptotics with error term for the second integral moments of families of automorphic L-functions for GL(2) over an arbitrary number field according to twists by idele characters with arbitrary…

Let $f$ be a Hecke-Maass cusp form for $SL_3(\mathbb{Z})$ and $\chi$ a primitive Dirichlet character of prime power conductor $\mathfrak{q}=p^{\kappa}$ with $p$ prime and $\kappa\geq 10$. We prove a subconvexity bound $$…

An automorphism on a complex supermanifold $\mathcal M$ is called unipotent if it reduces to the identity on the associated graded supermanifold $gr(\mathcal M)$. These automorphisms are close to be complementary to those responsible for…

We consider a special configuration in which a finite group $A$ acts by automorphisms on the finite group $G$, and the semidirect product $GA$ acts on the vector space $V$ by linear transformations; and discuss the existence of the regular…

The inversion formula is given for automorphisms of the Weyl algebras with polynomial coefficients over a field of characteristic zero. The theorem of Gabber on the degree of polynomial automorphism is extended. It is proved that any…

In this paper we prove that for any commutative (but in general non-associative) algebra $A$ with an invariant symmetric non-degenerate bilinear form there is a graded vertex algebra $V = V_0 \oplus V_2 \oplus V_3\oplus ...$, such that…

We give a fully explicit description of Lie algebra derivatives (generalizing raising and lowering operators) for representations of SL(3,R) in terms of a basis of Wigner functions. This basis is natural from the point of view of principal…

We study the question of whether the Morava K-theory of the classifying space of an elementary abelian group V is a permutation module (in either of two distinct senses) for the automorphism group of V. We use Brauer characters and computer…

We prove an orthogonality relation for the Fourier-Whittaker coefficients of a thin family of $GL(3)$ Maass forms containing all self-dual forms. This is obtained by analysing the Kuznetsov trace formula on $GL(3)$ for a certain family of…

Let $G$ be a reductive group over a number field $F$, which is split at a finite place $\mathfrak{p}$ of $F$, and let $\pi$ be a cuspidal automorphic representation of $G$, which is cohomological with respect to the trivial coefficient…

In this paper we study Clifford and harmonic analysis on some conformal flat spin manifolds. In particular we treat manifolds that can be parametrized by $U / \Gamma$ where $U$ is a simply connected subdomain of either $S^{n}$ or $R^{n}$…

We report on computations of the cohomology of GL_2(O_D) and SL_2(O_D), where D<0 is a fundamental discriminant. These computations go well beyond earlier results of Vogtmann and Scheutzow. We use the technique of homology of Voronoi…

We develop a (largely conjectural) theory of p-adic L-functions interpolating square roots of central L-values for automorphic forms on GSp(4) x GL(2) x GL(2), and a relation between these p-adic L-functions and families of Galois…

We establish an explicit formula for the character of an irreducible finite-dimensional representation of $\mathfrak{gl}(m|n)$. The formula is a finite sum with integer coefficients in terms of a basis $\mathcal{E}_{\mu}$ (Euler characters)…

This paper was motivated by a question of Avner Ash, asking if it is possible to construct non-selfdual, non-monomial, cuspidal cohomology classes for suitable congruence subgroups \Gamma of SL(n,\Z). Such a construction, in special…

Let $K$ be a field of characteristic different from 2 and let $G$ be a group. If the algebra $UT_n$ of $n\times n$ upper triangular matrices over $K$ is endowed with a $G$-grading $\Gamma: UT_n=\oplus_{g\in G}A_g$ we give necessary and…

We prove for L-function attached to an automorphic cusp form for the Hecke congruence group $\Gamma_0(D)$, which is also an eigenfunction of all the Hecke operators, that a positive proportion of its non-trivial zeros lie on the critical…