Related papers: Twisted Gan-Gross-Prasad conjecture for certain te…

In a recent paper, we defined twisted unitary $1$-groups and showed that they automatically induced error-detecting quantum codes. We also showed that twisted unitary $1$-groups correspond to irreducible products of characters thereby…

Let G be a real reductive Lie group with maximal compact sub- group K. We generalize the usual notion of Dirac index to a twisted version, which is nontrivial even in case G and K do not have equal rank. We compute ordinary and twisted…

We give the details of the construction of a map to restate a conjectural expression about adjoint group action on generic representations in L-packets. We give an application of the construction to give another proof of the classification…

In this note, we study the twisted Jacquet modules of sub-quotients of principal series representations of ${\rm GL}_2(D)$ where $D$ is a division algebra over a non-archimedean local field $F$. We begin with a proof of a conjecture due to…

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…

The twisted Gaussian Schell Model describes a family of partially coherent beams that present several interesting characteristics, and as such have attracted attention in classical and quantum optics. Recent techniques have been…

Let G/H be a unimodular real spherical space which is either absolutely spherical or wave-front. It is shown that every tempered representation of G/H embeds into a relative discrete series of a boundary degeneration of G/H. If in addition…

We establish an equality between two multiplicities: one in the restriction of tempered representations of a $p$-adic group to its closed subgroup with the same derived group; and one occurring in their corresponding component groups in…

The goal of this paper is to assign an intrinsic meaning to the space of quantum parameters $\operatorname{Par}_G$ appearing in the geometric Langlands program of Beilinson-Drinfeld. We introduce tame twistings, a variant of twisted…

We study representations of GL(n) appearing as quotients of a tensor of exceptional representations, in the sense of Kazhdan and Patterson. Such representations are called distinguished. We characterize distinguished principal series…

The tempered spectrum of the similitude groups of non-degenerate symplectic, hermitian, or split orthogonal forms defined over $p$\snug-adic groups of characteristic zero is studied. The components of representations induced from discrete…

We study the notion of twisted conjugacy separability (essentially introduced in our previous paper for a proof of twisted version of Burnside-Frobenius theorem) and some related properties. We give examples of groups with and without this…

In this paper, we give a full classification of the unitary dual of $G = U(n,2)$ for $n \geq 3$. As a consequence, we determine which of these representations are weakly fair $A_{\mathfrak{q}}(\lambda)$-modules or special unipotent…

Let $p$ be an odd prime, $m\in {\mathbb N}$ and set $q=p^m$, $G=\operatorname{PSL}_n(q)$. Let $\theta$ be a standard graph automorphism of $G$, $d$ be a diagonal automorphism and $\operatorname{Fr}_q$ be the Frobenius endomorphism of…

Let G be a simple algebraic group over an algebraically closed field of good odd characteristic, and let theta be an automorphism of G arising from an involution of its Dynkin diagram. We show that the spherical theta-twisted conjugacy…

In this paper we introduce the notion of twisted symplectic reflection algebras and describe the category of representations of such an algebra associated to a non-faithful G-action in terms of those for faithful actions of G.

In the present notes we introduce and study the twisted gamma-filtration on K_0(G), where G is a split simple linear algebraic group over a field of characteristic prime to the order of the center of G. We apply this filtration to construct…

Jet Tomography is proposed as a new test of Color Glass Condensate (CGC) initial conditions in non-central $A+A$ collisions. The $k_{T}$ factorized CGC formalism is used to calculate the rapidity twist in the reaction plane of both the bulk…

We demonstrate why for a sheared gas of hard spheres, described by the SLLOD equations with an iso-kinetic Gaussian thermostat in between collisions, deviations of the conjugate pairing rule for the Lyapunov spectrum are to be expected,…

Following Arthur's study of the representations of the orthogonal and symplectic groups, we prove many cases of both the local and global Arthur conjectures for tempered representations of the unitary group. This completes the proof of…