Related papers: A restriction problem for mod-$p$ representations …

Building on prior work, we analyze the decomposition of the restriction of an irreducible representation of SL_2(k), for k a p-adic field of odd residual characteristic, to a maximal compact subgroup K. The pattern of the decomposition…

We classify the irreducible, admissible, smooth, genuine mod p representations of the metaplectic double cover of SL(2,F), where F is a p-adic field and p is odd. We show, using a generalized Satake transform, that each such representation…

Let $p$ be a prime, and $F$ a non-archimedean local field with residue characteristic $p$ and ring of integers $\mathcal{O}_{F}$. Set $G_{S}:={\rm SL}_{2}(F)$and $K_{0}:={\rm SL}_{2}(\mathcal{O}_{F})$ . For a smooth irreducible…

Let F be a non-archimedean local field with residual characteristic p, and k an algebraically closed field with characteristic l, where l different from p. Let Rep_k(SL_n(F)) be the category of smooth k-representations of SL_n(F). In this…

For an arbitrary finite monoid $M$ and subgroup $K$ of the unit group of $M$, we prove that there is a bijection between irreducible representations of $M$ with nontrivial $K$-fixed space and irreducible representations of $\mathcal{H}_K$,…

Let $\bf T$ be the group of diagonal matrices in $SL_2(\bar{\mathbb{F}}_p)$, where $p$ is a prime number. Let $\Bbbk$ be an algebraically closed field of characteristic not equal to $2$ and $p$. We classify all the irreducible…

For infinite reductive groups with Frobenius maps, we show that certain subquotients of abstract representations of the groups induced from 1-dimensional representations of Borel subgroups are irreducible.

Let F be a non-Archimedean local field of residue characteristic p. In this paper, we first compute the reduction modulo p of irreducible smooth representations of a quaternion division algebra over F and of two-dimensional irreducible…

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 $k$…

In this note we determine the irreducible square integrable representations of a simple group which admits an admissible restriction to a subgroup $H$ locally isomorphic to $SL_2(\mathbb R).$ We show such representation is holomorphic and…

Let $\bbk$ be an algebraically closed field of prime characteristic $p$. If $p$ does not divide $n$, irreducible modules over $\frak {sl}_n$ for regular and subregular nilpotent representations have already known(see \cite{Jan2} and…

Let $p>2$ be a prime. We give examples of smooth absolutely irreducible representations of $\mathrm{GL}_2(\mathbb{Q}_{p^3})$ over $\mathbb{F}_{p^3}$ which are not admissible.

Let $F$ be a non-Archimedean locally compact field, let $G$ be a split connected reductive group over $F$. For a parabolic subgroup $Q\subset G$ and a ring $L$ we consider the $G$-representation on the $L$-module$$(*)\quad\quad\quad\quad…

Let $p$ be a prime number and $F$ a local field with residual characteristic $p$. In this article, to an irreducible smooth representation of $GL_2(F)$ over $\bar{\mathbf{F}}_p$ with central character, we associate canonically a diagram…

We determine the parahoric restriction of non-cuspidal irreducible smooth representations of GSp(4,F) for a local non-archimedean number field F.

The description of irreducible representations of a group G can be seen as a question in harmonic analysis; namely, decomposing a suitable space of functions on G into irreducibles for the action of G x G by left and right multiplication.…

Let F be a local field with finite residue field of characteristic p, D the quaternion division algebra with centre F, and R an algebraically closed field of any characteristic. We classify the smooth irreducible R-representations V of the…

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…

Let F_0 be a non-archimedean local field of odd residual characteristic and let G be the unramified unitary group U(2,2) defined over F_0. In this paper, we give a classification of the irreducible smooth representations of G of…

Let $F$ be a totally real field unramified at all places above $p$ and $D$ be a quaternion algebra which splits at either none, or exactly one, of the infinite places. Let $\bar{r}:\mathrm{Gal}(\bar{F}/F)\to…