Related papers: On the Gan-Gross-Prasad problem for finite unitary…

Let $(\mathcal{G},\nu)$ be a $t$-discrete ergodic groupoid. Consider a finite Von Neumann algebra $\mathcal{M}$ with separable predual. We prove that every uniformly bounded measurable representation $\rho:\mathcal{G} \rightarrow…

In this paper we give an algorithm to determine all finite matrix groups over a number field. Our algorithm is based on the representation theory of finite groups.

We construct extended Weil representations of unitary groups over finite fields geometrically, and show that they are Shintani lifts for Weil representations.

In a recent paper I defined a new basis for the Grothendieck group of unipotent representations of an almost simple Chevalley group over a finite field. The definition for classical types was different from that for exceptional types. In…

We present a uniform methodology for computing with finitely generated matrix groups over any infinite field. As one application, we completely solve the problem of deciding finiteness in this class of groups. We also present an algorithm…

In this article, we study connections between representation theory and efficient solutions to the conjugacy problem on finitely generated groups. The main focus is on the conjugacy problem in conjugacy separable groups, where we measure…

For a differential field $F$ having an algebraically closed field of constants, we analyze the structure of Picard-Vessiot extensions of $F$ whose differential Galois groups are unipotent algebraic groups and apply these results to study…

In this paper we discuss various aspects of the problem of determining the minimal dimension of an injective linear representation of a finite semigroup over a field. We outline some general techniques and results, and apply them to…

We prove a local Gan-Gross-Prasad conjecture on predicting the branching law for the non-tempered representations of general linear groups in the case of non-Archimedean field. We also generalize to Bessel and Fourier-Jacobi models and…

In this paper, we give a proof of the Gan-Gross-Prasad conjecture for the discrete series of U(p,q). Given a discrete series representation $D(\lambda)$ in terms of the Harish-Chandra parameter, the restriction of $D(\lambda)$ to U(p-1,q)…

We apply the orbit method to obtain formula for multiplicities of certain representations of unipotent groups over the finite field.

Let $G$ be a group and $H$ be a subgroup of $G$. The classical branching rule (or symmetry breaking) asks: For an irreducible representation $\pi$ of $G$, determine the occurrence of an irreducible representation $\sigma$ of $H$ in the…

Gaussian elimination answers any question about a finitely presented vector space. However, a "uniform family" of such presentations--given as generic relations among an unspecified number of generators--is susceptible to elimination only…

The Burnside Problem asks whether a finitely generated group of exponent n is finite. We present a solution for 2-generator groups of prime power exponent. Results of P. Hall and G. Higman extends the finiteness conclusion to groups having…

In this article we give an elementary introduction to the representation theory of finite magnetic groups from a purely mathematical point of view. -- En este art\'iculo damos una introducci\'on elemental a la teor\'ia de representaciones…

Preface (A.Vershik) - about these texts (3.); I.Interpolation between inductive and projective limits of finite groups with applicatons to linear groups over finite fields; II.The characters of the groups of almost triangle matrices over…

Every bi-uniform matroid is representable over all sufficiently large fields. But it is not known exactly over which finite fields they are representable, and the existence of efficient methods to find a representation for every given…

This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.

We state and prove an extension of the global Gan-Gross-Prasad conjecture and the Ichino-Ikeda conjecture to the case of some Eisenstein series on unitary groups $U_n\times U_{n+1}$. Our theorems are based on a comparison of the…

Let $G$ be a Lie group, and $H\subset G$ a closed subgroup. Let $\pi$ be an irreducible unitary representation of $G$. In this paper, we briefly discuss the orbit method and its application to the branching problem $\pi|_{H}$. We use the…