Related papers: Parabolic induction from two segments, linked unde…

We prove (under certain assumptions) the irreducibility of the limit $\sigma_2$ of a sequence of irreducible essentially self-dual Galois representations $\sigma_k: G_{\mathbf{Q}} \to \mathrm{GL}_4(\overline{\mathbf{Q}}_p)$ (as $k$…

Let $\pi_1,\ldots,\pi_k$ be smooth irreducible representations of $p$-adic general linear groups. We prove that the parabolic induction product $\pi_1\times\cdots\times \pi_k$ has a unique irreducible quotient whose Langlands parameter is…

A W-algebra is an associative algebra constructed from a semisimple Lie algebra and its nilpotent element. This paper concentrates on the study of 1-dimensional representations of these algebras. Under some conditions on a nilpotent element…

For a given finite index inclusion of conformal nets $\mathcal{B}\subset \mathcal{A}$ and a group $G < \mathrm{Aut}(\mathcal{A}, \mathcal{B})$, we consider the induction and the restriction procedures for $G$-twisted representations. We…

Let G be the F-points of a classical group defined over a p-adic field F of characteristic 0. We classify the irreducible unitarizable representation of G that are subquotients of the parabolic induction of cuspidal representations of Levi…

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…

We construct a new family of irreducible representations of $\mathcal{U}_q(\mathfrak{g}_\mathbb{R})$ and its modular double by quantizing the classical parabolic induction corresponding to arbitrary parabolic subgroups, such that the…

A complete invariant and a binary combination for irreducible representations of SL2(R) are introduced. With this, a new two-parameter family of representations is defined.

The unitary principal series representations of $G=GL(n,\mathbb{C})$ induced from a character of the maximal parabolic subgroup $P=(GL(1,\mathbb{C})\times GL(n-1,\mathbb{C}))\ltimes\mathbb{C}^{n-1}$ attain the minimal Gelfand--Kirillov…

We define a C*-hull for a *-algebra, given a notion of integrability for its representations on Hilbert modules. We establish a local-global principle which, in many cases, characterises integrable representations on Hilbert modules through…

In this article, we construct affine group schemes $GL(X)$ where $X$ is any object in the Verlinde category in characteristic $p$ and classify their irreducible representations. We begin by showing that for a simple object $X$ of…

We investigate the theory of induction in the setting of doubles of coideal $*$-subalgebras of compact quantum group Hopf $*$-algebras. We then exemplify parts of this theory in the particular case of quantum $SL(2,\mathbb{R})$, and compute…

In this paper, we obtain explicit branching laws for all irreducible unitary representations of $\Spin(N,1)$ restricted to a parabolic subgroup $P$. The restriction turns out to be a finite direct sum of irreducible unitary representations…

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…

We study degenerate principal series representations of the split real group $G_{2(2)}$ induced from a character of a maximal parabolic subgroup whose unipotent radical is a Heisenberg group. Using the Lie algebra action on the space of…

Given a measured space X with commuting actions of two groups G and H satisfying certain conditions, we construct a Hilbert C*(H)-module E(X) equipped with a left action of C*(G), which generalises Rieffel's construction of inducing…

The notion of permutative representation is generalized to the $2$-adic ring $C^*$-algebra $\mathcal{Q}_{2}$. Permutative representations of $\mathcal{Q}_2$ are then investigated with a particular focus on the inclusion of the Cuntz algebra…

Let $F$ be any non-Archimedean local field with a Galois involution $\sigma$ and $F_0$ be the fixed field for the action of $\sigma$. When the residue characteristic of $F_0$ is odd, using the explicit construction of cuspidal…

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…

Let $G$ be a complex reductive group and $H=G^{\theta}$ be its fixed point subgroup under a Galois involution $\theta$. We show that any $H$-distinguished representation $\pi$ (i.e $\mathrm{dim}_{\mathbb{C}}\left(\pi^{*}\right)^{H}\neq0$)…