Related papers: On self-dual simple types of $p$-adic classical gr…

In this article we consider a quaternionic inner form $G$ of a $p$-adic classical group defined over a non-archimedian local field of odd residue characteristic. We construct all full self-dual semisimple characters for $G$ and we classify…

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these…

We define semi-simple strata, semi-simple characters and semi-simple types in G_2(F). With some of these types we construct supercuspidal representations of this group.

We construct, for any symplectic, unitary or special orthogonal group over a locally compact nonarchimedean local field of odd residual characteristic, a type for each Bernstein component of the category of smooth representations, using…

Let $F$ be a non-Archimedean local field, $A$ be a central simple $F$-algebra, and $G$ be the multiplicative group of $A$. It is known that for every irreducible supercuspidal representation $\pi$, there exists a $[G, \pi]_{G}$-type $(J,…

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 $K$ be a $p$-adically closed field and $G$ a group interpretable in $K$. We show that if $G$ is definably semisimple (i.e. $G$ has no definable infinite normal abelian subgroups) then there exists a finite normal subgroup $H$ such that…

Let $G_n=\operatorname{GL}_n(F)$, where $F$ is a non-archimedean local field with residue characteristic $p$. Our starting point is the Bernstein-decomposition of the representation category of $G_n$ over an algebraically closed field of…

Let $p$ be an odd prime and let $G$ be a non-abelian finite $p$-group of exponent $p^2$ with three distinct characteristic subgroups, namely $1$, $G^p$, and $G$. The quotient group $G/G^p$ gives rise to an anti-commutative ${\mathbb…

We show that almost all (Bushnell and Kutzko) types of PGL(2,F), F a non-Archimedean locally compact field of odd residue characteristic, naturally appear in the cohomology of finite graphs.

Let k be a non-archimedean local field with residual characteristic p. Let G be a connected reductive group over k that splits over a tamely ramified field extension of k. Suppose p does not divide the order of the Weyl group of G. Then we…

Let $H$ be a finite quasisimple classical group, i.e. $H$ is perfect and $S:=H/Z(H)$ is a finite simple classical group. We prove in this paper that, excluding the cases when the simple group $S$ has a very exceptional Schur multiplier such…

Given a quaternionic form G of a p-adic classical group (p odd) we classify all cuspidal irreducible representations of G with coefficients in an algebraically closed field of characteristic different from p. We prove two theorems: At…

For a classical group over a non-archimedean local field of odd residual characteristic p, we construct all cuspidal representations over an arbitrary algebraically closed field of characteristic different from p, as representations induced…

In this paper, we give a uniform classification of the generic dual of quasi-split classical groups, their similitude counterparts, and general spin groups. As applications, for quasi-split classical groups, we show that the functorial…

Folloing the methods of Bushnell-Kutzko for general linear groups, we construct simple types attached to certain skew simple strata for a symplectic group and an unramified unitary group over a non-archimedean local field.

Let~$G$ be a unitary group of an~$\epsilon$-hermitian form~$h$ given over a nonarchimedean local field~$F_0$ of odd residue characteristic. We introduce a geometric combinatoric condition under which we prove "Intertwining implies…

Let $F$ be a non-archimedean locally compact field of residual characteristic $p$, let $G=\mathrm{GL}_{r}(F)$ and let $\widetilde{G}$ be an $n$-fold metaplectic cover of $G$ with $\mathrm{gcd}(n,p)=1$. We study the category…

We study infinite groups interpretable in power bounded $T$-convex, $V$-minimal or $p$-adically closed fields. We show that if $G$ is an interpretable definably semisimple group (i.e., has no definable infinite normal abelian subgroups)…

Given a grading by an abelian group G on a semisimple Lie algebra L over an algebraically closed field of characteristic 0, we classify up to isomorphism the simple objects in the category of finite-dimensional G-graded L-modules. The…