Related papers: Geometric side of a local relative trace formula

We generalize the notion of an approximate indicator for a closed subgroup $H$ of a locally compact group $G$ introduced by Aristov, Runde, and Spronk and extend their characterization of the existence of such nets in terms of the…

We conduct a systematic study of traces on locally compact groups, in particular traces on their universal and reduced C*-algebras. We introduce the trace kernel, and examine its relation to the von Neumann kernel and to small-invariant…

The notion of a \emph{$G$-completely reducible} subgroup is important in the study of algebraic groups and their subgroup structure. It generalizes the usual idea of complete reducibility from representation theory: a subgroup $H$ of a…

For an almost split Kac-Moody group G over a local non-archimedean field, the last two authors constructed a spherical Hecke algebra H (over the complex numbers C, say) and its Satake isomorphism with the commutative algebra of Weyl…

Let $E/F$ be a finite and Galois extension of non-archimedean local fields. Let $G$ be a connected reductive group defined over $E$ and let $M: = \mathfrak{R}_{E/F}\, G$ be the reductive group over $F$ obtained by Weil restriction of…

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,…

We establish the coarse relative trace formulae of Jacquet-Rallis for linear and unitary groups. Both formulae are of the form: a sum of spectral distributions equals a sum of geometric distributions. In order to obtain the spectral…

Let $F$ be a non Archimedean local field, and $G$ be the $F$-points of a connected quasi-split reductive group defined over $F$. In this note we propose a converse theorem statement for generic Langlands parameters of $G$ when the Langlands…

Let $F$ be a number field, $\pi$ either a unitary cuspidal automorphic representation of $\mathrm{GL}(2)/F$ or a unitary Eisenstein series, and $\chi$ a unitary Hecke character of analytic conductor $C(\chi).$ We develop a regularized…

In this paper, following the method developed by J.-L. Waldspurger and R. Beuzart-Plessis for Bessel models, we study two local relative trace formulas for the local twisted Gan-Gross-Prasad conjecture. By obtaining spectral expansions and…

Let $F$ be a non-Archimedean local field with odd characteristic $p$. Let $N$ be a positive integer and $G=Sp_{2N}(F)$. By work of Lomel\'i on $\gamma$-factors of pairs and converse theorems, a generic supercuspidal representation $\pi$ of…

A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…

We establish an infinitesimal version of the Jacquet-Rallis trace formula for general linear groups. Our formula is obtained by integrating a kernel truncated a la Arthur multiplied by the absolute value of the determinant to the power $s…

For a locally compact group $H$ with a left Haar measure, we study variable Lebesgue algebra $\mathcal{L}^{p(\cdot)}(H)$ with respect to a convolution. We show that if $\mathcal{L}^{p(\cdot)}(H)$ has bounded exponent, then it contains a…

We introduce a categorical framework for the study of representations of $G_F$, where $G$ is a reductive group, and $\bF$ is a 2-dimensional local field, i.e. $F=K((t))$, where $K$ is a local field. Our main result says that the space of…

Let $F$ be a $p$-adic field ($p\neq 2$), let $E$ be a quadratic Galois extension of $F$, and let $n \geq 2$. We construct representations in the discrete spectrum of the $p$-adic symmetric space $H \backslash G$, where $G =…

We develop uniform approximations for the trace formula for non-integrable systems in which SU(2) symmetry is broken by a non-linear term of the Hamiltonian. As specific examples, we investigate H\'enon-Heiles type potentials. Our formalism…

We generalize the concept of rigid inner forms, defined by Kaletha in [Kal16], to the setting of a local function field $F$ in order state the local Langlands conjectures for arbitrary connected reductive groups over $F$. To do this, we…

In this article we observe that a locally compact group $G$ is completely determined by the algebraic properties of its Feichtinger's Segal algebra $S_0(G).$ Let $G$ and $H$ be locally compact groups. Then any linear (not necessarily…

Let $E/F$ be an extension of number fields with $\mathrm{Gal}(E/F)$ simple and nonabelian. In [G] the first named author suggested an approach to nonsolvable base change and descent of automorphic representations of $\mathrm{GL}_2$ along…