Related papers: Blocks for mod $p$ representations of $GL_2(Q_p)$

In this article we show how certain irreducible unitary representation $ \Pi_\lambda $ of the twisted Heisenberg group $ \He_\lambda^n(\C)$ leads to the twisted modulation spaces $ M_\lambda^{p,q}(\R^{2n}).$ These $ \Pi_\lambda $ also turn…

Let $p$ be a prime number and $K$ a finite unramified extension of $\mathbb{Q}_p$. Building on recent work of Breuil, Herzig, Hu, Morra and Schraen, we study the smooth mod $p$ representations of $\mathrm{GL}_2(K)$ appearing in a tower of…

Let $\pi$ be a finite dimensional unitary representation of a group $G$ with a generating symmetric $n$-element set $S\subset G$. Fix $\vp>0$. Assume that the spectrum of $|S|^{-1}\sum_{s\in S} \pi(s) \otimes \overline{\pi(s)}$ is included…

The zig-zag conjecture says that the reductions of two-dimensional crystalline representations of the Galois group of ${\mathbb {Q}}_p$ of large exceptional weights and half-integral slopes up to $\frac{p-1}{2}$ vary through an alternating…

We count the connected components in the moduli space of PU(p,q)-representations of the fundamental group for a closed oriented surface. The components are labelled by pairs of integers which arise as topological invariants of the flat…

We determine the irreducible 2-modular representations of the symplectic group $G=Sp_{2n}(2)$ whose restriction to every abelian subgroup has a trivial constituent. A similar result is obtained for maximal tori of $G$. There is significant…

For a locally compact group $G$ and $p \in (1,\infty)$, we define $B_p(G)$ to be the space of all coefficient functions of isometric representations of $G$ on quotients of subspaces of $L_p$ spaces. For $p =2$, this is the usual…

The modular representation theory of the queer Lie superalgebra q(n) over characteristic p>2 is developed. We obtain a criterion for the irreducibility of baby Verma modules with semisimple p-characters and a criterion for the…

We study the crystalline universal deformation ring R (and its ideal of reducibility I) of a mod p Galois representation rho_0 of dimension n whose semisimplification is the direct sum of two absolutely irreducible mutually non-isomorphic…

Let $G$ be a split reductive group over a local field $\bK$, and let $G((t))$ be the corresponding loop group. In \cite{GK} we have introduced the notion of a representation of (the group of $\bK$-points) of $G((t))$ on a pro-vector space.…

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.

We describe the generic blocks in the category of smooth locally admissible mod $2$ representations of $\mathrm{GL}_2(\mathbb{Q}_2)$. As an application we obtain new cases of Breuil--M\'ezard and Fontaine--Mazur conjectures for…

Using differential techniques, we compute the Jacquet module of the locally analytic vectors of irreducible admissible unitary representations of GL_2(\qp). This gives a direct proof of some results of Colmez, leading to a proof of…

Let $G$ be a $p$-adic group which splits over an unramified extension and $Rep_{\Lambda}^{0}(G)$ the abelian category of smooth level $0$ representations of $G$ with coefficients in $\Lambda=\overline{\mathbb{Q}}_{\ell}$ or…

We consider smooth representations of the unit group $G = \mathcal{A}^{\times}$ of a finite-dimensional split basic algebra $\mathcal{A}$ over a non-Archimedean local field. In particular, we prove a version of Gutkin's conjecture, namely,…

Let $p$ be a prime number and $K$ a finite unramified extension of $\mathbb{Q}_p$. If $p$ is large enough with respect to $[K:\mathbb{Q}_p]$ and under mild genericity assumptions, we prove that the admissible smooth representations of…

Let $p$ be a prime such that $p \geq 5$. Let $G$ be a finite $p$-solvable group and let $p^a$ be the largest power of $p$ dividing $\chi(1)$ for an irreducible character $\chi$ of $G$, we show that $|G:F(G)|_p \leq p^{5.5a}$. Let $G$ be a…

Let $F$ be a non-archimedean locally compact field of residue characteristic $p\neq2$, let $G=\mathrm{GL}_{n}(F)$ and let $H$ be an orthogonal subgroup of $G$. For $\pi$ a complex smooth supercuspidal representation of $G$, we give a full…

Let $F$ be a totally real field in which $p$ is unramified and $B$ be a quaternion algebra which splits at at most one infinite place. Let $\overline{r}:\mathrm{Gal}(\overline{F}/F)\to \mathrm{GL}_2(\overline{\mathbb{F}}_p)$ be a modular…

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…