Related papers: Unitarizability in generalized rank three for clas…

For p odd, the Lie group SO_0(p+1,p+1) has a family of unitary degenerate principal series representations realized on the space of real (p+1) by (p+1) skew symmetric matrices, similar to the Stein's complementary series for SL(2n,C) or…

Let G be the group of rational points of a connected reductive group over a finite field. Based on work of Lusztig and Yun, we make the Jordan decomposition for irreducible G-representations canonical. It comes in the form of an equivalence…

Let $G$ be a connected, simply connected nilpotent group and $\pi$ be a square-integrable irreducible unitary representation modulo its center $Z(G)$ on $L^2(\mathbf{R}^d)$. We prove that under reasonably weak conditions on $G$ and $\pi$…

In this talk we discuss the relations between representations of algebraic groups and principal bundles on algebraic varieties, especially in characteristic $p$. We quickly review the notions of stable and semistable vector bundles and…

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…

We study irreducible odd mod $p$ Galois representations $\bar{\rho} \colon \mathrm{Gal}(\overline{F}/F) \to G(\overline{\mathbb{F}}_p)$, for $F$ a totally real number field and $G$ a general reductive group. For $p \gg_{G, F} 0$, we show…

We study, for a locally compact group $G$, the compactifications $(\pi,G^\pi)$ associated with unitary representations $\pi$, which we call {\it $\pi$-Eberlein compactifications}. We also study the Gelfand spectra $\Phi_{\mathcal{A}}(\pi)}$…

Let F be a non-Archimedean locally compact field with residual characteristic p, let G be an inner form of GL(n,F) for a positive integer n and let R be an algebraically closed field of characteristic different from p. When R has…

Let $G$ be a locally compact group with an open subgroup $H$ with the Kunze-Stein property, and let $\pi$ be a unitary representation of $H$. We show that the representation $\widetilde{\pi}$ of $G$ induced from $\pi$ is an…

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 $q$…

Let $G$ be a real classical group (including the real metaplectic group). We consider a nilpotent adjoint orbit $\check{\mathcal O}$ of $\check G$, the Langlands dual of $G$ (or the metaplectic dual of $G$ when $G$ is a real metaplectic…

Let $(\pi, \mathcal{H})$ be a strongly continuous unitary representation of a 1-connected Lie group $G$ such that the Lie algebra $\mathfrak{g}$ of $G$ is generated by the positive cone $C_\pi := \{x \in \mathfrak{g} : -i\partial \pi(x)…

This paper examines fields of rationality in families of cuspidal automorphic representations of unitary groups. Specifically, for a fixed $A$ and a sufficiently large family $\mathcal{F}$, a small proportion of representations $\pi\in…

We study the notion of irreducibility of semigroup morphisms. Given an alphabet $\Sigma$, a morphism $\varphi:\Sigma^+\rightarrow\Sigma^+$ is irreducible if any factorisation $\varphi=\psi_2\circ\psi_1$ can only be satisfied if $\psi_1$ or…

Let F be a finite extension of Q_p. Using the mod p Satake transform, we define what it means for an irreducible admissible smooth representation of an F-split p-adic reductive group over \bar F_p to be supersingular. We then give the…

We consider the following question, concerning associative algebras R over an algebraically closed field k: When can the space of (equivalence classes of) finite dimensional irreducible representations of R be topologically embedded into a…

We present a finite algorithm for computing the set of irreducible unitary representations of a real reductive group G. The Langlands classification, as formulated by Knapp and Zuckerman, exhibits any representation with an invariant…

We study the irreducible complex representations of general linear groups over principal ideal local rings of length two with a fixed finite residue field. We construct a canonical correspondence between the irreducible representations of…

The work of Bernstein-Zelevinsky and Zelevinsky gives a good understanding of irreducible subquotients of a reducible principal series representation of $GL_n(F)$, $F$ a $p$-adic field (without specifying their multiplicities which is done…

We study irreducible unitary \reps of $U_q(SO(2,1))$ and $U_q(SO(2,3))$ for $q$ a root of unity, which are finite dimensional. Among others, unitary \reps corresponding to all classical one-particle representations with integral weights are…