Related papers: Unitary dual of quasi-split $PGSO_8^E$

Minimal unitary representation of SO*(8) = SO(6,2) realized over the Hilbert space of functions of five variables and its deformations labeled by the spin t of an SU(2) subgroup correspond to massless conformal fields in six dimensions as…

We show that the cotangent bundle $T^*(G/K)$ of a quasi-split symmetric space $G/K$ is isomorphic to the dual variety of the loop symmetric space for the Langlands dual group, providing instances of the relative Langlands duality for…

In this paper, we study Lie superalgebras of $2\times 2$ matrix-valued first-order differential operators on the complex line. We first completely classify all such superalgebras of finite dimension. Among the finite-dimensional…

We introduce the notion of quasi-Poisson modules over Lie-Rinehart pairs and prove that for the Lie-Rinehart pair $(\dot A,\dot\fk)$ in which $\dot A=\bbbc[t_1^{\pm1},\ldots,t_m^{\pm1}]\ot\Lam_n$ and $\dot\fk={\rm Der}(\dot A)$, there is a…

The goal of this paper is to prove how Arthur's results, in the case of split odd orthogonal p-adic groups, imply the Langlands' classification of discrete series. Of course this need the validity of ''fundamental'' lemmas which are not yet…

In this paper, we highlight and state precisely the local Langlands correspondence for quasi-split O_{2n} established by Arthur. We give two applications: Prasad's conjecture and Gross--Prasad conjecture for O_{n}. Also, we discuss the…

We consider supersymmetric grand unified theory (GUT) with the gaugino mediated supersymmetry breaking and investigate a possibility to discriminate different GUT models in terms of predicted sparticle mass spectra. Taking two example GUT…

Substantial progress has recently been reported in the determination of the Hilbert-Schmidt (HS) separability probabilities for two-qubit and qubit-qutrit (real, complex and quaternionic) systems. An important theoretical concept employed…

Multiplicative Unitaries are described in terms of a pair of commuting shifts of relative depth two. They can be generated from ambidextrous Hilbert spaces in a tensor C*-category. The algebraic analogue of the Takesaki-Tatsuuma Duality…

We construct a quasi-particle basis of the integrable highest weight module of highest weight $3\Lambda_0$ for the twisted affine Lie algebra of type $A_2^{(2)}$ in the principal realization. More specifically, by introducing the concept of…

In this article, we present algorithms for computing parabolic inductions and Jacquet modules for the general linear group $G$ over a non-Archimedean local field. Given the Zelevinsky data or Langlands data of an irreducible smooth…

Let $F$ be a locally compact non-Archimedean field of characteristic $0$, and let $G$ be either the split special orthogonal group $\mathrm{SO}_{2n+1}(F)$ or the symplectic group $\mathrm{Sp}_{2n}(F)$. The goal of this paper is to give an…

In [5] and [19], the authors gave anomaly cancellation formulas for the gauge groups E8,E8*E8. In this paper, we mainly deal with the case of gauge group E8*E8*E8. Using the E8*E8*E8 bundle, we construct some modular forms over SL2(Z). By…

In this paper we establish the endoscopic classification of tempered representations of quasi-split unitary groups over local fields, and the endoscopic classification of the discrete automorphic spectrum of quasi-split unitary groups over…

Let KG be a group algebra of a finite p-group G over a finite field K of characteristic p. We compute the order of the unitary subgroup of the group of units when G is either an extraspecial 2-group or the central product of such a group…

We apply the super duality formalism recently developed by the authors to obtain new equivalences of various module categories of general linear Lie superalgebras. We establish the correspondence of standard, tilting, and simple modules, as…

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…

We consider semiclassical orthogonal polynomials on the unit circle associated with a weight function that satisfy a Pearson-type differential equation involving two polynomials of degree at most three. Structure relations and difference…

Let G be a connected, simply connected Poisson-Lie group with quasitriangular Lie bialgebra g. An explicit description of the double D(g) is given, together with the embeddings of g and g^*. This description is then used to provide a…

We study $R$-groups for $p$-adic inner forms of quasi-split special unitary groups. We prove Arthur's conjecture, the isomorphism between the Knapp-Stein $R$-group and the Langlands-Arthur $R$-group, for quasi-split special unitary groups…