Related papers: Simple supercuspidal representations of $\mathrm{G…

Let $F$ be the function field of a projective smooth geometrically connected curve $X$ defined over a finite field $\mathbb{F}_q$. Let $G$ be a split semisimple algebraic group over $\mathbb{F}_q$. Let $S$ be a non-empty finite set of…

We perform a general analysis of representations of the superconformal algebras OSp(8/4,R) and OSp(8*/2N) in harmonic superspace. We present a construction of their highest-weight UIR's by multiplication of the different types of massless…

F(4) supergravity, the gauge theory of the exceptional six-dimensional Anti-de Sitter superalgebra, is coupled to an arbitrary number of vector multiplets whose scalar components parametrize the quaternionic manifold SO(4,n)/SO(4)\times…

Brumer and Kramer gave bounds on local conductor exponents for an abelian variety $A/\mathbb Q$ in terms of the dimension of $A$ and the localization prime $p$. Here we give improved bounds in the case that $A$ has maximal real…

Let $G$ be a reductive group over a nonarchimedean local field $F$. In the quest for a classification of irreducible smooth representations of $G$, it is critical to understand the case of supercuspidal representations -- those whose matrix…

An orthogonal basis of weight vectors for a class of infinite-dimensional representations of the orthosymplectic Lie superalgebra osp(2m+1|2n) is introduced. These representations are particular lowest weight representations V(p), with a…

We prove that regular supercuspidal representations of $p$-adic groups are uniquely determined by their character values on very regular elements -- a special class of regular semisimple elements on which character formulae are very simple…

Let F be a finite extension of Qp and G be GL(2,F). When V is the tensor product of three admissible, irreducible, finite dimensional representations of G, the space of G-invariant linear forms has dimension at most one. When a non zero…

We study the compatibility of the formal degree conjecture and the parabolic induction process in the simplest nontrivial case for quasi-split $p$-adic groups. For a generic discrete series $\pi$ induced from an irreducible supercuspidal…

We study a problem concerning parabolic induction in certain $p$-adic unitary groups. More precisely, for $E/F$ a quadratic extension of $p$-adic fields the associated unitary group $G=\mathrm{U}(n,n+1)$ contains a parabolic subgroup $P$…

For a central division algebra $D$ of dimension $d^2$ over a finite extension $F$ of $\mathbb Q_p$ or of $\mathbb F_p((t))$, a field $R$ of characteristic prime to $p$, and an irreducible smooth $R$-representation $\pi$ of $G=GL_n(D)$, we…

Let $X$ be a set of $4$ generic points in $\mathbb{P}^2$ with homogeneous coordinate ring $R$. We classify indecomposable graded MCM modules over $R$ by reducing the classification to the Four Subspace problem solved by Nazarova and…

In the first part of this paper we study minimal representations of simply connected simple split groups of type $D_k$ or $E_k$ over local non-archimedian fields. Our main result is an explicit formula for the spherical vectors in these…

A well known result of Borel says that the category of modules over the Iwahori-Hecke algebra of a semisimple p-adic group G describes the Bernstein component associated to the unramified principal series of G. We consider Bernstein…

A paper of Reeder-Yu gives a construction of epipelagic supercuspidal representations of $p$-adic groups. The input for this construction is a pair $(\lambda, \chi)$ where $\lambda$ is a stable vector in a certain representation coming from…

Let $F$ be a locally compact non-archimedean field of residue characteristic $p$, $\textbf{G}$ a connected reductive group over $F$, and $R$ a field of characteristic $p$. When $R$ is algebraically closed, the irreducible admissible…

We prove that if the space of newforms is non-zero for every irreducible generic supercuspidal representation of ${\rm SO}_{2n+1}$ then it is also non-zero for all irreducible generic representations of ${\rm SO}_{2n+1}$.

We study irreducible representations of two classes of conformal Galilei algebras in 1-spatial dimension. We construct a functor which transforms simple modules with nonzero central charge over the Heisenberg subalgebra into simple modules…

Let E/Q be a real quadratic field and pi_0 a cuspidal, irreducible, automorphic representation of GL(2,A_E) with trivial central character and infinity type (2,2n+2) for some non-negative integer n. We show that there exists a non-zero…

We prove that any connected reductive group of semisimple $F$-rank 1 over a $p$-adic field admits an irreducible admissible supersingular mod-$p$ representation. This establishes one of the missing cases in Vign\'eras' existence proof for…