Related papers: Test vectors for some ramified representations

Let G denote either a special orthogonal group or a symplectic group defined over the complex numbers. We prove the following saturation result for G: given dominant weights \lambda^1, ..., \lambda^r such that the tensor product…

Toric varieties associated with root systems appeared very naturally in the theory of group compactifications. Here they are considered in a very different context. We prove the vanishing of higher cohomology groups for certain line bundles…

We describe a special case of base change of certain supercuspidal representations from a ramified unitary group to a general linear group, both defined over a p-adic field of odd residual characteristic. Roughly speaking, we require the…

Let E be a division ring and G a finite group of automorphisms of E whose elements are distinct modulo inner automorphisms of E. Given a representation \rho: B-> GL(d,E) of an F-algebra B, we give necessary and sufficient conditions for…

Let $G$ be a split reductive $p$-adic Lie group. This paper is the first in a series on the construction of locally analytic $G$-representations which do not lie in the principal series. Here we consider the case of the general linear group…

We wish to give a new proof of one of the main results of Atkin and Lehner. Their theory depends, among other things, on a theorem characterizing forms in S_k(Gamma_0(N)) whose Fourier coefficients satisfy a certain vanishing condition. Our…

Let $\Gamma$ be a finite group acting on a simple Lie algebra $\mathfrak{g}$ and acting on a $s$-pointed projective curve $(\Sigma, \vec{p}=\{p_1, \dots, p_s\})$ faithfully (for $s\geq 1$). Also, let an integrable highest weight module…

Let $p>0$ be a prime, $G$ be a finite $p$-group and $\Bbbk$ be an algebraically closed field of characteristic $p$. Dave Benson has conjectured that if $p=2$ and $V$ is an odd-dimensional indecomposable representation of $G$ then all…

Let $G$ be a $p$-adic group that splits over an unramified extension. We decompose $Rep_{\Lambda}^{0}(G)$, the abelian category of smooth level $0$ representations of $G$ with coefficients in $\Lambda=\overline{\mathbb{Q}}_{\ell}$ or…

We apply some recent developments of Baldoni-Beck-Cochet-Vergne on vector partition function, to Kostant's and Steinberg's formulae, for classical Lie algebras $A\_r$, $B\_r$, $C\_r$, $D\_r$. We therefore get efficient {\tt Maple} programs…

In this paper we generalise the notion of Drinfeld modular form for the group $\Gamma$ := GL2(Fq[$\theta$]) to a vector-valued setting, where the target spaces are certain modules over positive characteristic Banach algebras over which are…

To prove that a measure, linearly representable by means of a finite set of nonnegative matrices $\mathcal M$, has the weak-Gibbs property, one check the uniform convergence (on $\mathcal M^\mathbb N$) of the sequence of vectors…

We show that the multiple divisor functions of integers in invertible residue classes modulo a prime number, as well as the Fourier coefficients of GL(N) Maass cusp forms for all N larger than 2, satisfy a central limit theorem in a…

Let $\mathbf{G}$ be a connected reductive algebraic group over an algebraic closure $\overline{\mathbb{F}_p}$ of the finite field of prime order $p$ and let $F : \mathbf{G} \to \mathbf{G}$ be a Frobenius endomorphism with $G = \mathbf{G}^F$…

We introduce the theory of unipotent morphisms of algebraic stacks and prove a surprising local to global principle for a class of vector bundles. Two sample applications of our methods are the following: (1) a unipotent analogue of…

Weighted projective lines, introduced by Geigle and Lenzing in 1987, are important objects in representation theory. They have tilting bundles, whose endomorphism algebras are the canonical algebras introduced by Ringel. The aim of this…

Let P be a parabolic subgroup of a semisimple complex Lie group G defined by a subset \Sigma of simple roots of G, and let E_\phi be a homogeneous vector bundle over the flag manifold G/P corresponding to a linear representation \phi of P.…

To each Drinfeld module over a finitely generated field with generic characteristic, one can associate a Galois representation arising from the Galois action on its torsion points. Recent work of Pink and R\"utsche has described the image…

We present a Serre-type conjecture on the modularity of four-dimensional symplectic mod p Galois representations. We assume that the Galois representation is irreducible and odd (in the symplectic sense). The modularity condition is…

We give a new construction of tensor product gamma factors for a pair of irreducible representations of $\operatorname{GL}_c\left(\mathbb{F}_q\right)$ and $\operatorname{GL}_k\left(\mathbb{F}_q\right)$. This construction is a finite field…