Related papers: Representations of a $p$-adic group in characteris…

Let $p$ be a prime. Given a split semisimple group scheme $G$ over a normal integral domain $R$ which is a faithfully flat $\mathbb Z_{(p)}$-algebra, we classify all finite dimensional representations $V$ of the fiber $G_K$ of $G$ over…

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

We study representations of the classical infinite dimensional real simple Lie groups $G$ induced from factor representations of minimal parabolic subgroups $P$. This makes strong use of the recently developed structure theory for those…

Let $\mathbf{G}$ be an algebraic group over a local field $\mathbf k$ of characteristic zero. We show that the locally compact group $\mathbf G(\mathbf k)$ consisting of the $\mathbf k$-rational points of $\mathbf G$ is of type I. Moreover,…

Let G be a simple algebraic group defined over an algebraically closed field k of characteristic p>0. Here we classify all irreducible kG-modules for which the principal A1 has no repeated composition factors, extending the work of…

Let $G$ be a $p$-adic reductive group. We determine the extensions between admissible smooth mod $p$ representations of $G$ parabolically induced from supersingular representations of Levi subgroups of $G$, in terms of extensions between…

Let $G$ be a connected reductive group over a totally real field $F$ which is compact modulo center at archimedean places. We find congruences modulo an arbitrary power of p between the space of arbitrary automorphic forms on $G(\mathbb…

Let p be a prime number, and F a nonarchimedean local field of residual characteristic p. We explore the interaction between the pro-p-Iwahori-Hecke algebras of the group GL_n(F) and its derived subgroup SL_n(F). Using the interplay between…

Let G be a branch group (as defined by Grigorchuk) acting on a tree T. A parabolic subgroup P is the stabiliser of an infinite geodesic ray in T. We denote by $\rho_{G/P}$ the associated quasi-regular representation. If G is discrete, these…

For W a finite (2-)reflection group and B its (generalized) braid group, we determine the Zariski closure of the image of B inside the corresponding Iwahori-Hecke algebra. The Lie algebra of this closure is reductive and generated in the…

Let F be a non-archimedean local field with residue characteristic p. Let l be a prime number different from p. Let G be a connected reductive group which is split, semi-simple, and simply connected. On the one hand, we describe the…

Let $W$ be a vector space over an algebraically closed field $k$. Let $H$ be a quasisimple group of Lie type of characteristic $p\ne {\rm char}(k)$ acting irreducibly on $W$. Suppose also that $G$ is a classical group with natural module…

Let $F$ be a non Archimedean local field with odd residual characteristic, and let $K$ be a hyperspecial maximal compact subgroup of the $p$-adic symplectic group $G=\mathrm{Sp}_4(F)$. Let $\mathfrak{s}$ be an inertial class for $G$ in the…

We study finite-dimensional representations of hyper loop algebras, i.e., the hyperalgebras over an algebraically closed field of positive characteristic associated to the loop algebra over a complex finite-dimensional simple Lie algebra.…

Let $G$ be a simple algebraic group over an algebraically closed field $K$ of characteristic $p\geqslant 0$, let $H$ be a proper closed subgroup of $G$ and let $V$ be a nontrivial irreducible $KG$-module, which is $p$-restricted, tensor…

Let $K$ be a non-discrete non-Archimedean local field with residue characteristic $p$. Let $G$ be the group of $K$ rational points of a algebraic connected reductive group defined over $K$. In this article we compute the extensions between…

In this paper we express certain multiplicities in modular representation-theoretic categories of type A in terms of affine p-Kazhdan-Lusztig polynomials. The representation-theoretic categories we deal with include the categories of…

Let $\mathbb{F}$ be an algebraically closed field and $G$ be an almost quasi-simple group. An important problem in representation theory is to classify the subgroups $H<G$ and $\mathbb{F} G$-modules $L$ such that the restriction…

In this paper we give a simple (local) proof of two principal results about irreducible tempered representations of general linear groups over a non-archimedean local division algebra. We give a proof of the parameterization of the…

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…