Related papers: Endoscopic character identities for depth-zero sup…

Let F be a non-archimedean local field, of characteristic 0. Let V be a finite dimensional vector space over F and q be a non-degenerate quadratic form on V. Denote d the dimension of V and G=SO(d) the special orthogonal group of (V,q). Let…

Cuspidal representations of a reductive p-adic group G over a field of characteristic different from p are relatively injective and projective with respect to extensions that split by a U-equivariant linear map for any subgroup U that is…

We investigate the local descents for special orthogonal groups over p-adic local fields of characteristic zero, and obtain an explicit spectral decomposition of the local descents at the first occurrence index in terms of the local…

Given an open set with finite perimeter $\Omega\subset \mathbb{R}^n$, we consider the space $LD_\gamma^{p}(\Omega)$, $1\leq p<\infty$, of functions with $p$th-integrable deformation tensor on $\Omega$ and with $p$ th-integrable trace value…

We study randomly coloured graphs embedded into Euclidean space, whose vertex sets are infinite, uniformly discrete subsets of finite local complexity. We construct the appropriate ergodic dynamical systems, explicitly characterise ergodic…

It is known by a result of Mendes and Sampaio that the Lipschitz normal embedding of a subanalytic germ is fully characterized by the Lipschitz normal embedding of its link. In this note, we show that the result still holds for definable…

Local Binary Pattern (LBP) is a traditional descriptor for texture analysis that gained attention in the last decade. Being robust to several properties such as invariance to illumination translation and scaling, LBPs achieved…

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 $G=\mathrm{U}(n,n)$ contains a parabolic subgroup $P$ with…

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…

We construct a surjective map from the set of conjugacy classes of depth-zero cuspidal enhanced L-parameters to that of isomorphism classes of depth-zero supercuspidal representations for simple adjoint groups, and check the bijectivity in…

We prove microlocal estimates at the trapped set of asymptotically Kerr spacetimes: these are spacetimes whose metrics decay inverse polynomially in time to a stationary subextremal Kerr metric. This combines two independent results. The…

This is a sequel to [Xu18] on the $L$-packets of quasisplit general symplectic and even orthogonal groups. We show the existence of global $L$-packets and establish the functoriality of endoscopic transfer for them in many cases.

We give a purely local proof of the explicit Local Langlands Correspondence for $\mathrm{GSp}_4$ and $\mathrm{Sp}_4$. Moreover, we give a unique characterization in terms of stability of $L$-packets and other properties. Finally, in the…

Physical transformations are described by linear maps that are completely positive and trace preserving (CPTP). However, maps that are positive (P) but not completely positive (CP) are instrumental to derive separability/entanglement…

In this paper, we prove the geometric expansion of a local twisted trace formula for the Whittaker induction of any symmetric pairs that are coregular. This generalizes the local (twisted) trace formula for reductive groups proved by Arthur…

We discuss progress towards the classification of irreducible admissible representations of reductive groups over non-archimedean local fields and the local Langlands correspondence. We also state some (partly conjectural) compatibility…

Let $F$ be a non-Archimedean local field of characteristic $0$, let $G$ be the group of $F$-rational points of a connected reductive group defined over $F$ and let $G'$ be the group of $F$-rational points of its quasi-split inner form.…

We derive new singular value decompositions and range characterizations for the X-ray transform on the Poincar\'e disk, intertwining relations with distinguished differential operators of wedge type, and a surjectivity result for the…

In this work, we explicitly compute a certain family of twisted gamma factors of a simple supercuspidal representation $\pi$ of a $p$-adic odd orthogonal group. These computations, together with analogous computations for general linear…

We study some tempered endoscopic cases of Langlands functoriality on the $n$-variable unitary groups via the simple stable trace formula. This extends previous work of Rogawski and Clozel-Harris-Labesse. Ramakrishnan and Kim-Shahidi have…