A classification of subgroups of odd unitary groups

2018 ◽  
Vol 46 (9) ◽  
pp. 3795-3805 ◽  
Author(s):  
Weibo Yu ◽  
Yaya Li ◽  
Hang Liu
Keyword(s):  
Unitary Groups

scholarly journals ENDOSCOPY AND COHOMOLOGY IN A TOWER OF CONGRUENCE MANIFOLDS FOR

2019 ◽  
Vol 7 ◽  
Author(s):  
SIMON MARSHALL ◽  
SUG WOO SHIN
Keyword(s):  
Symmetric Spaces ◽  
Unitary Groups ◽  
Automorphic Representations ◽  
Locally Symmetric Spaces ◽  
Hermitian Forms ◽  
Work In Progress ◽  
Endoscopic Classification

By assuming the endoscopic classification of automorphic representations on inner forms of unitary groups, which is currently work in progress by Kaletha, Minguez, Shin, and White, we bound the growth of cohomology in congruence towers of locally symmetric spaces associated to$U(n,1)$. In the case of lattices arising from Hermitian forms, we expect that the growth exponents we obtain are sharp in all degrees.

scholarly journals Local Langlands correspondence for unitary groups via theta lifts

2021 ◽  
Vol 25 (30) ◽  
pp. 861-896
Author(s):  
Rui Chen ◽  
Jialiang Zou
Keyword(s):  
Unitary Groups ◽  
Irreducible Representations ◽  
Theta Correspondence ◽  
Langlands Correspondence ◽  
Alternative Approach ◽  
Local Langlands Correspondence

Using the theta correspondence, we extend the classification of irreducible representations of quasi-split unitary groups (the so-called local Langlands correspondence, which is due to Mok) to non quasi-split unitary groups. We also prove that our classification satisfies some good properties, which characterize it uniquely. In particular, this paper provides an alternative approach to the works of Kaletha-Mínguez-Shin-White and Mœglin-Renard.

Type classification of extreme quantized characters

2019 ◽  
Vol 41 (2) ◽  
pp. 593-605
Author(s):  
RYOSUKE SATO
Keyword(s):  
Dynamical Systems ◽  
Quantum Groups ◽  
Asymptotic Representation ◽  
Operator Algebras ◽  
Complete Solution ◽  
Unitary Groups ◽  
Inductive System ◽  
Von Neumann ◽  
Type Classification

The notion of quantized characters was introduced in our previous paper as a natural quantization of characters in the context of asymptotic representation theory for quantum groups. As in the case of ordinary groups, the representation associated with any extreme quantized character generates a von Neumann factor. From the viewpoint of operator algebras (and measurable dynamical systems), it is natural to ask what is the Murray–von Neumann–Connes type of the resulting factor. In this paper, we give a complete solution to this question when the inductive system is of quantum unitary groups $U_{q}(N)$.

ON -DISTINGUISHED REPRESENTATIONS OF THE QUASI-SPLIT UNITARY GROUPS

2019 ◽  
pp. 1-52 ◽  
Author(s):  
A. Mitra ◽  
Omer Offen
Keyword(s):  
Unitary Group ◽  
Discrete Series ◽  
Large Family ◽  
Quadratic Extension ◽  
Base Change ◽  
Unitary Groups ◽  
Distinguished Representations ◽  
Tempered Representation

We study $\text{Sp}_{2n}(F)$ -distinction for representations of the quasi-split unitary group $U_{2n}(E/F)$ in $2n$ variables with respect to a quadratic extension $E/F$ of $p$ -adic fields. A conjecture of Dijols and Prasad predicts that no tempered representation is distinguished. We verify this for a large family of representations in terms of the Mœglin–Tadić classification of the discrete series. We further study distinction for some families of non-tempered representations. In particular, we exhibit $L$ -packets with no distinguished members that transfer under base change to $\text{Sp}_{2n}(E)$ -distinguished representations of $\text{GL}_{2n}(E)$ .

scholarly journals Structure of Hyperbolic Unitary Groups II: Classification of E-Normal Subgroups

2017 ◽  
Vol 24 (02) ◽  
pp. 195-232 ◽  
Author(s):  
Raimund Preusser
Keyword(s):  
Unitary Group ◽  
Direct Limit ◽  
Finite Ring ◽  
Unitary Groups ◽  
Normal Subgroups ◽  
Finite Rings ◽  
Elementary Subgroup ◽  
Rings With Involution ◽  
Hyperbolic Unitary Group

This paper proves the sandwich classification conjecture for subgroups of an even dimensional hyperbolic unitary group [Formula: see text] which are normalized by the elementary subgroup [Formula: see text], under the condition that R is a quasi-finite ring with involution, i.e., a direct limit of module finite rings with involution, and [Formula: see text].

scholarly journals RAISING THE LEVEL OF AUTOMORPHIC REPRESENTATIONS OF OF UNITARY TYPE

2021 ◽  
pp. 1-24
Author(s):  
Christos Anastassiades ◽  
Jack A. Thorne
Keyword(s):  
Unitary Groups ◽  
Automorphic Representations ◽  
Endoscopic Classification

Abstract We use the endoscopic classification of automorphic representations of even-dimensional unitary groups to construct level-raising congruences.

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