Related papers: The local converse theorem for quasi-split $O_{2n}…

Rallis and Soudry have proven the stability under twists by highly ramified characters of the local gamma factor arising from the doubling method, in the case of a symplectic group or orthogonal group G over a local non-archimedean field F…

We prove the local Gross-Prasad conjecture for tempered representations of special orthogonal groups. Roughly speaking, the conjecture says that, if sigma is an irreducible representation of SO(n) and rho is an irreducible representation of…

We derive a collective field theory of the singlet sector of the Sp(2N) sigma model. Interestingly the hamiltonian for the bilocal collective field is the same as that of the O(N) model. However, the large-N saddle points of the two models…

We study O(n)-symmetric two-dimensional conformal field theories (CFTs) for a continuous range of n below two. These CFTs describe the fixed point behavior of self-avoiding loops. There is a pair of known fixed points connected by an RG…

Let $K$ be a complete discretely valued field with the residue field $\kappa$. Assume that cohomological dimension of $\kappa$ is less than or equal to $1$ (for example, $\kappa$ is an algebraically closed field or a finite field). Let $F$…

The local Langlands correspondence for GL(n) of a non-Archimedean local field $F$ parametrizes irreducible admissible representations of $GL(n,F)$ in terms of representations of the Weil-Deligne group $WD_F$ of $F$. The correspondence,…

Behind this sophisticated title hides an elementary exercise on Clifford theory for index two subgroups and self-dual/conjugate-dual representations. When applied to semi-simple representations of the Weil-Deligne group $W'_F$ of a non…

The present paper is devoted to the description of local and 2-local automorphisms on Cayley algebras over an arbitrary field $\mathbb{F}$. Given a Cayley algebra $\mathcal{C}$ with norm $n$, let $O(\mathcal{C},n)$ be the corresponding…

Let $\Gamma \stackrel{i}{\hookrightarrow} L$ be a lattice in the real simple Lie group $L$. If $L$ is of rank at least 2 (respectively locally isomorphic to $Sp(n,1)$) any unbounded morphism $\rho: \Gamma \longrightarrow G$ into a simple…

We investigate the particle and kinetic-energy densities for a system of $N$ fermions bound in a local (mean-field) potential $V(\bfr)$. We generalize a recently developed semiclassical theory [J. Roccia and M. Brack, Phys. Rev.\ Lett. {\bf…

Let G be a connected reductive group defined over a non-archimedean local field of characteristic 0. We assume G is quasi-split, adjoint and absolutly simple. Let g be the Lie algebra of G. We consider the space of the invariant…

Let $F$ be a non-Archimedean local field. Let $\Cal W_F$ be the Weil group of $F$ and $\Cal P_F$ the wild inertia subgroup of $\scr W_F$. Let $\hat{\Cal W}_F$ be the set of equivalence classes of irreducible smooth representations of $\Cal…

Let $F$ be a non-Archimedean locally compact field. We show that the local Langlands correspondence over $F$ has a strong property generalizing the higher ramification theorem of local class field theory. If $\pi$ is an irreducible cuspidal…

In this partly expository paper we discuss conditions for the global injectivity of $C^2$ semi-algebraic local diffeomorphisms $f:\mathbb{R}^n \to \mathbb{R}^n$. In case $n > 2$, we consider the foliations of $\mathbb{R}^n$ defined by the…

We study the variation of the local Langlands correspondence for ${\rm GL}_{n}$ in characteristic-zero families. We establish an existence and uniqueness theorem for a correspondence in families, as well as a recognition theorem for when a…

In this article, we give a new method for proving Howe correspondence in the case of dual pairs of type $({\rm GL}_n, {\rm GL}_m)$ over a non-Archimedean locally compact field $F$. The proof consists in combining a study on Kudla's…

In this note we study several topics related to the schema of local reflection $\mathsf{Rfn}(T)$ and its partial and relativized variants. Firstly, we introduce the principle of uniform reflection with $\Sigma_n$-definable parameters,…

We extend Pisier's abstract version of Grothendieck's theorem to general non-locally convex quasi-Banach spaces. We also prove a related result on factoring operators through a Banach space and apply our results to the study of…

We study the validity of the local theta correspondence over a non-archimedean local field in the context of modular representation theory \textit{i.e.} for representations with coefficient fields of positive characteristic. For a…

Among connected linear algebraic groups, quasi-reductive groups generalize pseudo-reductive groups, which in turn form a useful relaxation of the notion of reductivity. We study quasi-reductive groups over non-archimedean local fields,…