Related papers: Twisted character of a small representation of GL(…

We compute by a purely local method the elliptic, twisted by transpose-inverse, character \chi_\pi of the representation \pi=I_{(3,1)}(1_3) of PGL(4,F) normalizedly induced from the trivial representation of the maximal parabolic subgroup…

We provide a purely local computation of the (elliptic) twisted (by "transpose-inverse") character of the representation \pi=I(\1) of PGL(3) over a p-adic field induced from the trivial representation of the maximal parabolic subgroup. This…

We show that the Gelfand character $ \chi_G$ of a finite group $G $ (i.e. the sum of all irreducible complex characters of $G$ ) may be realized as a `` twisted trace'' $ g \mapsto Tr( \rho_g \circ T) $ for a suitable involutive linear…

Let $F$ be a non-archimedean local field of characteristic zero, let $(\pi,V)$ be an irreducible, admissible representation of $\GSp(4,F)$ with trivial central character, and let $\chi$ be a quadratic character of $F^\times$ with conductor…

Let $G_\cpl$ be a connected complex reductive Lie group, and $G$ be a real form. Let $(\pi,V)$ be a finite-dimensional irreducible representation of $G$. Assume $(\pi,V)$ admits a $G$ invariant hermitian form. {In…

Consider an irreducible, admissible representation $\pi$ of GL(2,$F$) whose restriction to GL(2,$F)^+$ breaks up as a sum of two irreducible representations $\pi_+ + \pi_-$. If $\pi=r_{\theta}$, the Weil representation of GL(2,$F$) attached…

Let $F$ be a non-archimedean local field of characteristic different from $2$ and $G$ be either an odd special orthogonal group ${\rm SO}_{2r+1}(F)$ or a symplectic group ${\rm Sp}_{2r}(F)$. In this paper, we establish the local converse…

Fix $n \geq 2$ an integer, and let $F$ be a totally real number field. We derive estimates for the finite parts of the $L$-functions of irreducible cuspidal $\operatorname{GL}_n({\bf{A}}_F)$-automorphic representations twisted by class…

Let $F$ be a non-archimedean local field of residue characteristic $p$, $G$ be the group $GL(n, F)$. In this note, under the assumption $(n, p)=1$, we show a simple cuspidal representation $\pi$ (that with normalized level $\frac{1}{n}$) of…

Let $\text{E}/\text{F}$ be a quadratic extension of non-Archimedean local fields with odd residual characteristic. In this paper, we give equivalent conditions for a simple supercuspidal representation $\pi$ of $\text{GL}(n, \text{E})$ to…

Let n be a positive integer, F be a non-Archimedean locally compact field of odd residue characteristic p and G be an inner form of GL(2n,F). This is a group of the form GL(r,D) for a positive integer r and division F-algebra D of reduced…

We obtain explicit formulas for the test vector in the Bessel model and derive the criteria for existence and uniqueness for Bessel models for the unramified, quadratic twists of the Steinberg representation \pi of GSp(4,F), where F is a…

Let $\pi$ be a $SL(3,\mathbb{Z})$ Hecke-Maass cusp form, $f$ be a $SL(2,\mathbb{Z})$ holomorphic cusp form or Maass cusp form and $\chi$ be any non-trivial character $\bmod \, p$, where $p$ is prime. We show that the $L$-function associated…

Let $G$ be a group with subgroup $H$, and let $(\pi,V)$ be a complex representation of $G$. The natural action of the normalizer $N$ of $H$ in $G$ on the space $\mathrm{Hom}_H(\pi,\mathbb{C})$ of $H$-invariant linear forms on $V$, provides…

In this paper, we consider the (partial) symmetric square $L$-function $L^S(s,\pi,Sym^2\otimes\chi)$ of an irreducible cuspidal automorphic representation $\pi$ of $\GL_r(\A)$ twisted by a Hecke character $\chi$. In particular, we will show…

Let $q \in \mathbb{Z} [i]$ be prime and $\chi $ be the primitive quadratic Hecke character modulo $q$. Let $\pi$ be a self-dual Hecke automorphic cusp form for $\mathrm{SL}_3 (\mathbb{Z} [i] )$ and $f$ be a Hecke cusp form for $\Gamma_0 (q)…

In this paper, we compute the conjugacy classes and the list of irreducible characters of GSp(4,q), where q is odd. We also determine precisely which irreducible characters are non-cuspidal and which are generic. These characters are then…

Let $\mathbf{G}$ be a connected reductive algebraic group over a $p$-adic local field $F$. In this paper we study the asymptotic behaviour of the trace characters $\theta _{\pi}$ evaluated at a regular element $\gamma $ of $\mathbf{G}(F)$…

Let $F$ be a non-Archimedean local field with odd characteristic $p$. Let $N$ be a positive integer and $G=Sp_{2N}(F)$. By work of Lomel\'i on $\gamma$-factors of pairs and converse theorems, a generic supercuspidal representation $\pi$ of…

We establish an explicit formula for twisted Harish-Chandra characters of toral supercuspidal representations of p-adic reductive groups under several technical assumptions. Our setup especially includes the case of a quasi-split group…