Related papers: On local integrability results for $p$-adic reduct…

In this paper, we study local regularity properties of minimizers of nonlocal variational functionals with variable exponents and weak solutions to the corresponding Euler--Lagrange equations. We show that weak solutions are locally bounded…

In this expository article, we outline a basic theory of group (co)homology and prove a cohomological formulation of the Local Reciprocity Law: $${\rm Gal}(L/K)^{\rm ab} \cong H_T^{-2}({\rm Gal}(L/K),\mathbb{Z}) \cong H_T^{0}({\rm…

We study locally compact groups having all dense subgroups (locally) minimal. We call such groups densely (locally) minimal. In 1972 Prodanov proved that the infinite compact abelian groups having all subgroups minimal are precisely the…

In this paper, we prove the local converse theorem for $\textrm{Sp}_{2r}(F)$ over a $p$-adic field $F$. More precisely, given two irreducible supercuspidal representations of $\textrm{Sp}_{2r}(F)$ with the same central character such that…

Harish-Chandra induction and restriction functors play a key role in the representation theory of reductive groups over finite fields. In this paper, extending earlier work of Dat, we introduce and study generalisations of these functors…

A locally compact group $G$ has the factorization property if the map $$C^*(G)\odot C^*(G)\ni a\otimes b\mapsto \lambda(a)\rho(b)\in\mathcal B(L^2(G))$$ is continuous with respect to the minimal C*-norm. This paper seeks to initiate a…

The theory of locally analytic representations of $p$-adic Lie groups with $\mathbf{Q}_p$-coefficients is a powerful tool in $p$-adic Hodge theory and in the $p$-adic Langlands program. This perspective reveals important differential…

Pairs $\aa \subset \bb$ of local quantum field theories are studied, where $\aa$ is a chiral conformal \qft and $\bb$ is a local extension, either chiral or two-dimensional. The local correlation functions of fields from $\bb$ have an…

One proves the Crew-Tsuzuki "p-adic local monodromy conjecture" (for local fields of characteristic p>0).

We use the progenerator constructed in our previous paper to give a necessary condition for a simple module of a finite reductive group to be cuspidal, or more generally to obtain information on which Harish-Chandra series it can lie in. As…

Let F be a finite field with q elements, let A be a finite dimensional F-algebra and let J=J(A) be the Jacobson radical of A. Then G=1+J is a p-group, where p is the characteristic of F. We refer to G as an F-algebra group. A subgroup H of…

Given a supercuspidal representation $\sigma$ of a parabolic subgroup $P$ of reductive group $G$, we discover a universal hierarchical structure of reducibility of the parabolic induction $Ind^G_P(\sigma)$, i.e. always irreducible from some…

Let $G$ be a real reductive linear group in the Harish-Chandra class. Suppose that $P$ is a parabolic subgroup of $G$ with Langlands decomposition $P=MAN$. Let $\pi$ be an irreducible representation of the Levi factor $L=MA$. We give…

The local $h$-polynomial was introduced by Stanley as a fundamental enumerative invariant of a triangulation $\Delta$ of a simplex. This polynomial is known to have nonnegative and symmetric coefficients and is conjectured to be…

Let $L/K$ be a finite Galois extension of local fields. The Hasse-Arf theorem says that if Gal$(L/K)$ is abelian then the upper ramification breaks of $L/K$ must be integers. We prove the following converse to the Hasse-Arf theorem: Let $G$…

In this note, we provide several characterizations of regular local rings in positive characteristics, in terms of the Hilbert-Kunz multiplicity and its higher $\tor$ counterparts $\i t_i=\underset{n \to \infty}{\lim} \l(\tor_i(k,{}^{f^n}…

The irreducible characters of a finite reductive group are partitioned into Harish-Chandra series that are labelled by cuspidal pairs. In this note, we describe how one can algorithmically calculate those cuspidal pairs using results of…

We prove that local weak solutions to nonlocal parabolic $p$-Laplace equations are locally Lipschitz continuous in space, uniformly in time for every $1<p<\infty$ and $s \in (0,1)$ whenever $sp > p-1$. Our results hold for symmetric,…

Given a discrete group $\Gamma$, a finite factor $\mathcal N$ and a real number $p\in [1, +\infty)$ with $p\neq 2,$ we are concerned with the rigidity of actions of $\Gamma$ by linear isometries on the $L_p$-spaces $L_p(\mathcal N)$…

We prove that a (globally) subanalytic p-adic function which is locally Lipschitz continuous with some constant C is piecewise (globally on each piece) Lipschitz continuous with possibly some other constant, where the pieces can be taken…