We generalize [6, Theorem 3] to a Mackey-type formula for the compact restriction of a semisimple perverse sheaf produced by parabolic induction from a character sheaf, under certain conditions on the parahoric group scheme used to define compact restriction. This provides new tools for matching character sheaves with admissible representations.

Abstract As a continuation of [9], this paper studies scattered representations $SO(2n+1, {{\mathbb{C}}})$, $Sp(2n, and $SO(2n, {{\mathbb{C}}})$. We describe the Zhelobenko parameters these representations, count their cardinality, determine spin-lowest $K$-types. also disprove conjecture raised in 2015 asserting that unitary dual can be obtained via parabolic induction from irreducible with no...

1.1. Shan has proved that the categories Oc(Wn) for rational Cherednik algebras of type Wn = W (G(`, 1, n)) = Snn(μ`) with n varying, together with decompositions of the parabolic induction and restriction functors of Bezrukavnikov-Etingof, provide a categorification of an integrable s̃le Fock space representation F(m), [18]. The parameters m ∈ Z` and e ∈ N ∪ {∞} arise from the choice of paramet...

We study a problem concerning parabolic induction in certain p-adic unitary groups. More precisely, for $E/F$ quadratic extension of fields the associated group $G=\mathrm{U}(n,n)$ contains subgroup $P$ with Levi component $L$ isomorphic to $\mathrm{GL}_n(E)$. Let $\pi$ be an irreducible supercuspidal representation depth zero. use Hecke algebra methods determine when parabolically induced $\io...

We give a necessary and sufficient condition for pair of parabolic subgroups $P$ $Q$ $G=GL_n(\mathbb{R})$ such that the tensor product any two unitarily induced representations from are tempered. also an $L^p$-estimate matrix coefficients regular on $L^2(G/L)$ when $L$ is Levi subgroup $G$.

We construct algebra homomorphisms from affine Yangians to the current algebras of rectangular W-algebras both in type A. The construction is given via coproduct and evaluation map for Yangians. As a consequence, we show that parabolic inductions representations can be regarded as tensor product under homomorphisms. same method applicable also super-setting.

Because it is not clear that the induction of orthostatic intolerance in returning astronauts always requires prolonged exposure to microgravity, we investigated orthostatic tolerance and autonomic cardiovascular function in 16 healthy subjects before and after the brief micro- and hypergravity of parabolic flight. Concomitantly, we investigated the effect of parabolic flight-induced vomiting o...

The quantum supergroup OSPq(1|2n) is studied systematically. A Haar functional is constructed, and an algebraic version of the Peter Weyl theory is extended to this quantum supergroup. Quantum homogeneous superspaces and quantum homogeneous supervector bundles are defined following the strategy of Connes’ theory. Parabolic induction is developed by employing the quantum homogeneous supervector ...

This course consists of two parts. In the first we will study representations of reductive groups over local non-archimedian fields [ such as Qp and Fq((s))]. In this part I’ll closely follow the notes of the course of J.Bernstein. Moreover I’ll often copy big chanks from these notes. In the second the representations of reductive groups over 2-dimensional local fields [ such as Qp((s))]. In th...