Related papers: Unitarizability in generalized rank three for clas…

We study irreducibility of Galois representations $\rho_{\pi,\lambda}$ associated to a $n=7$ or 8-dimensional regular algebraic essentially self-dual cuspidal automorphic representation $\pi$ of $\text{GL}_n(\mathbb{A}_\mathbb{Q})$. We show…

This paper gives a complete classification of the unitary irreducible spherical representations of split real and p-adic groups. The results were obtained around 2000, the changes to the new version are expository.

Let v be the right regular representation of a compact quantum group G. Then (S.L.Woronowicz, "Compact quantum groups") v contains all irreducible representations of G and each irreducible representation enters v with the multiplicity equal…

We classify the irreducible representations of smooth, connected affine algebraic groups over a field, by tackling the case of pseudo-reductive groups. We reduce the problem of calculating the dimension for pseudo-split pseudo-reductive…

Let $G$ be an inner form of a general linear group or classical group over a non-archimedean local field of residual characteristic $p$, assumed odd in the classical case. We prove that every smooth representation of $G$ over an…

In this paper, we determine the composition series of the induced representation $\delta([\nu^{\frac{1}{2}}\rho,\nu^c\rho])\times \delta([\nu^{-a}\rho,\nu^b\rho]) \rtimes \sigma$ where $a, b, c \in \mathbb{Z}+\frac{1}{2}$ such that…

In this paper, we determine the composition series of the induced representation $\delta([\nu^{-a}\rho,\nu^{c}\rho]) \times \delta([\nu^{\frac{1}{2}}\rho, \nu^{b}\rho]) \rtimes \sigma $ where $a, b, c \in \mathbb{Z}+ \frac{1}{2} $ such that…

We prove that any reductive group G over a non-Archimedean local field has a cuspidal complex representation.

Assume $G$ is a connected reductive algebraic group defined over $\bar{\mathbb{F}_p}$ such that $p$ is good prime for $G$. Furthermore we assume that $Z(G)$ is connected and $G/Z(G)$ is simple of classical type. Let $F$ be a Frobenius…

Let $F$ be a local field with residue characteristic $p$, let $C$ be an algebraically closed field of characteristic $p$, and let $\mathbf{G}$ be a connected reductive $F$-group. In a previous paper, Florian Herzig and the authors…

A method to construct irreducible unitary representations of a hyperspecial compact subgroup of a reductive group over p-adic field with odd p is presented. Our method is based upon Cliffods theory and Weil representations over finite…

Let H be any reductive p-adic group. We introduce a notion of cuspidality for enhanced Langlands parameters for H, which conjecturally puts supercuspidal H-representations in bijection with such L-parameters. We also define a cuspidal…

For a classical group over a non-archimedean local field of odd residual characteristic p, we prove that two cuspidal types, defined over an algebraically closed field C of characteristic different from p, intertwine if and only if they are…

Let $G$ be a finite classical group of Lie type of rank $\ell$, defined over a field of characteristic $p>2$. In this work, we classify the irreducible representations of $G$ whose dimensions are bounded by a constant proportional to…

Let $G$ be a connected reductive group over a finite field $\mathfrak{f}$ of order $q$. When $q$ is small, we make further assumptions on $G$. Then we determine precisely when $G(\mathfrak{f})$ admits irreducible, cuspidal representations…

Let $F$ be a global field. Let $G$ and $H$ be two connected reductive group defined over $F$ endowed with an $F$-morphism $f: H\rightarrow G$ such that the induced morphism $H_{der}\rightarrow G_{der}$ on the derived groups is a central…

We construct all cuspidal l-modular representations of a unitary group in three variables attached to an unramified extension of local fields of odd residual characteristic p with l\neq p. We describe the l-modular principal series and show…

In this paper, we consider representations of $p$-adic classical groups parabolically induced from the products of shifted Speh representations and unitary representations of Arthur type of good parity. We describe how to compute the socles…

Let $E/F$ be a unramified quadratic extension of non-archimedean local fields of odd characteristic $p$, and $G$ be the unramified unitary group $U(2, 1)(E/F)$. For an irreducible smooth representation $\pi$ of $G$ over…

Given a supercuspidal representation $\sigma$ of a parabolic subgroup $P$ of reductive group $G$, we discover a universal hierarchical structure of reducibility of the parabolic induction $Ind^G_P(\sigma)$, i.e. always irreducible from some…