Related papers: Some results on reducibility of parabolic inductio…

Higher Deligne-Lusztig representations are virtual smooth representations of parahoric subgroups in a $p$-adic group. They are natural analogs of classical Deligne-Lusztig representations of reductive groups over finite fields. The most…

In its most general formulation a quantum kinematical system is described by a Heisenberg group; the "configuration space" in this case corresponds to a maximal isotropic subgroup. We study irreducible models for Heisenberg groups based on…

Let $F$ be a non-archimedean local field of characteristic zero. We study theta correspondence for (complex) representations of symplectic--even orthogonal dual reductive pairs over $F;$ more specifically, the big theta lifts. We prove…

Let $G$ be a connected reductive $p$-adic group and let $\theta$ be an automorphism of $G$ of order at most two. Suppose $\pi$ is an irreducible smooth representation of $G$ that is taken to its dual by $\theta$. The space $V$ of $\pi$ then…

A group is irreducibly represented if it has a faithful irreducible unitary representation. For countable groups, a criterion for irreducible representability is given, which generalises a result obtained for finite groups by W. Gasch\"utz…

An analogue of Burnside's Lemma for 2-transitive groups is shown to hold for a class of topological groups. If the group is compact the representation is finite and splits into an irreducible and the constant functions. If both the group…

Let $\rho$ f,$\lambda$ be the residual Galois representation attached to a newform f and a prime ideal $\lambda$ in the integer ring of its coefficient field. In this paper, we prove explicit bounds for the residue characteristic of the…

Among connected linear algebraic groups, quasi-reductive groups generalize pseudo-reductive groups, which in turn form a useful relaxation of the notion of reductivity. We study quasi-reductive groups over non-archimedean local fields,…

In this article, we examine the restriction of the metaplectic representation $\pi$ over a $p$-adic field $k$, $p\neq2$, of zero characteristic to an isotropic torus $S$ contained in the symplectic group. First we give necessary and…

A parametrization of irreducible representations associated with a regular adjoint orbit of a classical group over finite quotient rings of the ring of integer of a non-dyadic non-archimedean local field is presented. The parametrization is…

Let $E/F$ be a quadratic extension of $p$-adic fields and let $d$, $m$ be nonnegative integers of distinct parities. Fix admissible irreducible tempered representations $\pi$ and $\sigma$ of $GL_d(E)$ and $GL_m(E)$ respectively. We assume…

The canonical dimension is an invariant attached to admissible representations of p-adic reductive groups, which has only received significant attention in the case of mod-p representations. In the case of complex representations, the…

An algebra group over a field $F$ is a group of the form $G = 1+J$ where $J$ is a finite-dimensional nilpotent associative $F$-algebra. A theorem of M. Boyarchenko asserts that, in the case where $F$ is a non-archimedean local field, every…

In this paper we prove the following. Let $\Sigma$ be an $n$--dimensional closed hyperbolic manifold and let $g$ be a Riemannian metric on $\Sigma \times \mathbb{S}^1$. Given an upper bound on the volumes of unit balls in the Riemannian…

A parabolic subalgebra $\mathfrak{p}$ of a complex semisimple Lie algebra $\mathfrak{g}$ is called a parabolic subalgebra of abelian type if its nilpotent radical is abelian. In this paper, we provide a complete characterization of the…

Let $G$ be a simple algebraic group over an algebraically closed field $K$ of characteristic $p > 0$. We consider connected reductive subgroups $X$ of $G$ that contain a given distinguished unipotent element $u$ of $G$. A result of…

Let $G$ be a simple algebraic group over an algebraically closed field $K$ of characteristic $p\geqslant 0$, let $H$ be a proper closed subgroup of $G$ and let $V$ be a nontrivial irreducible $KG$-module, which is $p$-restricted, tensor…

Parahoric group schemes are certain possibly non-reductive, smooth, affine integral models of reductive group schemes defined over a henselian discretely valued field $K$ whose residue field is perfect. We show that any such group scheme…

This paper deals with sufficiency conditions for irreducibility of certain induced modules. We also construct irreducible representations for a group $G$ over a field ${\mathbb K}$ where the group $G$ is a semidirect product of a normal…

We classify globally irreducible representations of alternating groups and double covers of symmetric and alternating groups. In order to achieve this classification we also completely characterise irreducible representations of such groups…