Related papers: Partitions of single exterior type

We prove Breuil's conjecture concerning the reduction modulo $p$ of trianguline representations $V$ and of the representations $\Pi(V)$ of $\mathrm{GL}_2(\mathbf{Q}_p)$ associated to them by the $p$-adic Langlands correspondence. The main…

For a connected quasi-split reductive algebraic group $G$ over a field $k$, which is either a finite field or a non-archimedean local field, $\theta$ an involutive automorphism of $G$ over $k$, let $K =G^\theta$. Let $K^1=[K^0,K^0]$, the…

Let $G=\text{GL}_n(q)$ be the general linear group over the finite field $\mathbb{F}_q$ of $q$ elements, and let $k$ be an algebraically closed field of characteristic $r >0$ such that $r$ does not divide $q(q-1)$. In 1999, Cline, Parshall,…

Let A be a finite dimensional central division algebra over a local non-archimedean field F. Fix any parabolic subgroup P of GL(n,A) and a Levi factor M of P. Let \pi be an irreducible unitary representation of M and \phi (not necessarily…

Let $G$ be one of the classical Lie groups $\GL_{n+1}(\R)$, $\GL_{n+1}(\C)$, $\oU(p,q+1)$, $\oO(p,q+1)$, $\oO_{n+1}(\C)$, $\SO(p,q+1)$, $\SO_{n+1}(\C)$, and let $G'$ be respectively the subgroup $\GL_{n}(\R)$, $\GL_{n}(\C)$, $\oU(p,q)$,…

Using the general framework of polynomial representations defined by Doty and generalizing the definition given by Doty, Nakano and Peters for $G = \mathrm{GL}_n$, we consider polynomial representations of $G_r T$ for an arbitrary closed…

This thesis is devoted to the study of the interactions existing between the algebraic structure of locally compact groups and the properties of their continuous unitary representations, with a special emphasis on the Type I groups. On the…

Let F be a non Archimedean locally compact field and let D be a central F-division algebra. We prove that any positive level supercuspidal irreducible representation of the group GL(m,D) is compactly induced from a representation of a…

We construct an L^2-model of "very small" irreducible unitary representations of simple Lie groups G which, up to finite covering, occur as conformal groups Co(V) of simple Jordan algebras V. If $V$ is split and G is not of type A_n, then…

Let $G$ be a connected reductive algebraic group defined over a finite field $\mathbb{F}_q$. In the 1980s, Kawanaka introduced the generalized Gelfand-Graev representations (GGGRs for short) of the finite group $G^F$ in the case where $q$…

The tensor square conjecture states that for $n \geq 10$, there is an irreducible representation $V$ of the symmetric group $S_n$ such that $V \otimes V$ contains every irreducible representation of $S_n$. Our main result is that for large…

We prove a conjecture for the irreducibility of singular Gelfand-Tsetlin modules. We describe explicitly the irreducible subquotients of certain classes of singular Gelfand-Tsetlin modules.

The unitary dual of $GL(n, \mathbb{R})$ was classified by Vogan in the 1980s. Focusing on the irreducible unitary representations of $GL(n, \mathbb{R})$ with half-integral infinitesimal characters, we find that Speh representations and the…

Let $\rho$ be an $n$-dimensional representation of $\mathcal{G}_{\mathbb{Q}_p}$ over $\overline{\mathbb{F}_p}$. When $\rho$ is generic and a good conjugate, the article "Conjectures and results on modular representations of…

Let $G$ be an inner form of a general linear group over a non-archimedean locally compact field of residue characteristic $p$, let $R$ be an algebraically closed field of characteristic different from $p$ and let $\mathscr{R}_R(G)$ be the…

Given a quaternionic form G of a p-adic classical group (p odd) we classify all cuspidal irreducible representations of G with coefficients in an algebraically closed field of characteristic different from p. We prove two theorems: At…

New presentations of Specht modules of symmetric groups over fields of characteristic zero have been obtained by Brauner, Friedmann, Hanlon, Stanley and Wachs. These involve generators that are column tabloids and relations that are Garnir…

In this paper, we study a class of generalized intersection matrix Lie algebras $\gim(M_n)$, and prove that its every finite-dimensional semi-simple quotient is of type $M(n,{\bf a}, {\bf c},{\bf d})$. Particularly, any finite dimensional…

We summarize the recent results about complete solvability of Hermitian and rectangular complex matrix models. Partition functions have very simple character expansions with coefficients made from dimensions of representation of the linear…

Let G be a connected simple adjoint p-adic group not isomorphic to a projective linear group PGL(m,D) of a division algebra D, or an adjoint ramified unitary group of a split hermitian form in 3 variables. We prove that G admits an…