Related papers: Stable Klingen Vectors and Paramodular Newforms

Let E/Q be a real quadratic field and pi_0 a cuspidal, irreducible, automorphic representation of GL(2,A_E) with trivial central character and infinity type (2,2n+2) for some non-negative integer n. We show that there exists a non-zero…

Let $F$ be a $p$-adic field and $(\pi, V)$ an irreducible complex representation of $G=GSp(4, F)$ with trivial central character. Let ${\rm Si}(\mathfrak{p}^2)\subset G$ denote the Siegel congruence subgroup of level $\mathfrak{p}^2$ and…

Let $F$ be a non-archimedean local field of characteristic zero and $(\pi, V)$ a depth zero, irreducible, supercuspidal representation of $GSp(4, F)$. We calculate the dimensions of the spaces of Klingen-invariant vectors in $V$ of level…

We prove several dimension formulas for spaces of scalar-valued Siegel modular forms of degree $2$ with respect to certain congruence subgroups of level $4$. In case of cusp forms, all modular forms considered originate from cuspidal…

This paper is a continuation of the author's previous wotk. We supplement four results on a family of holomorphic Siegel cusp forms for $GSp_4/\mathbb{Q}$. First, we improve the result on Hecke fields. Namely, we prove that the degree of…

We consider four classes of classical groups over a non-archimedean local field F: symplectic, (special) orthogonal, general (s)pin and unitary. These groups need not be quasi-split over F. The main goal of the paper is to obtain a local…

We give several resolutions of the Steinberg representation St_n for the general linear group over a principal ideal domain, in particular over Z. We compare them, and use these results to prove that the computations in [AGM4] are…

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…

We obtain explicit formulas for the test vector in the Bessel model and derive the criteria for existence and uniqueness for Bessel models for the unramified, quadratic twists of the Steinberg representation \pi of GSp(4,F), where F is a…

We construct analogues of the Hecke operators for the moduli space of G-bundles on a curve X over a local field F with parabolic structures at finitely many points. We conjecture that they define commuting compact normal operators on the…

We describe the image of general families of two-dimensional representations over compact semi-local rings. Applying this description to the family carried by the universal Hecke algebra acting on the space of modular forms of level $N$…

We investigate a Dirichlet series involving the Fourier-Jacobi coefficients of two cusp forms $F,G$ for orthogonal groups of signature $(2,n+2)$. In the case when $F$ is a Hecke eigenform and $G$ is a Maass lift of a Poincar\'e series, we…

Let $F$ be an arbitrary totally real field. Under weak conditions we prove the existence of certain Eisenstein congruences between parallel weight $k \geq 3$ Hilbert eigenforms of level $\mathfrak{mp}$ and Hilbert Eisenstein series of level…

We characterize the space of new forms for $\Gamma_0(m)$ as a common eigenspace of certain Hecke operators which depend on primes $p$ dividing the level $m$. To do that we find generators and relations for a $p$-adic Hecke algebra of…

We investigate some key analytic properties of Fourier coefficients and Hecke eigenvalues attached to scalar-valued Siegel cusp forms $F$ of degree 2, weight $k$ and level $N$. First, assuming that $F$ is a Hecke eigenform that is not of…

Let $K := \mathrm{GL}_n(\mathcal{O})$ denote the maximal compact subgroup of $\mathrm{GL}_n(F)$, where $F$ is a nonarchimedean local field with ring of integers $\mathcal{O}$. We study the decomposition of the space of locally constant…

This paper gives a classification of stable vectors in dual Vinberg representations coming from a graded Lie algebra of type $F_4$ in a way that is independent of the field of definition. Relating these gradings to Moy-Prasad filtrations,…

A main goal of this paper is to introduce a new description of the stable orbital integral for a regular semisimple element and for the unit element of the Hecke algebra in the case of $\mathfrak{gl}_{n,F}$, $\mathfrak{u}_{n,F}$, and…

We develop and collect techniques for determining Hochschild cohomology of skew group algebras S(V)#G and apply our results to graded Hecke algebras. We discuss the explicit computation of certain types of invariants under centralizer…

Let $F \in S_{k_1}(\Gamma^{(2)}(N_1))$ and $G \in S_{k_2}(\Gamma^{(2)}(N_2))$ be two Siegel cusp forms over the congruence subgroups $\Gamma^{(2)}(N_1)$ and $\Gamma^{(2)}(N_2)$ respectively. Assume that they are Hecke eigenforms in…