The Weil Character of the Unitary Group Associated to a Finite Local Ring

2002 ◽  
Vol 54 (6) ◽  
pp. 1229-1253 ◽  
Author(s):  
Roderick Gow ◽  
Fernando Szechtman
Keyword(s):  
Local Ring ◽  
Unitary Group ◽  
Quadratic Extension ◽  
Weil Representation ◽  
Finite Local Ring

AbstractLetR/R be a quadratic extension of finite, commutative, local and principal rings of odd characteristic. Denote byUn(R) the unitary group of ranknassociated toR/R. The Weil representation ofUn(R) is defined and its character is explicitly computed.

scholarly journals UNITARY GROUPS OVER LOCAL RINGS

2013 ◽  
Vol 13 (02) ◽  
pp. 1350093 ◽  
Author(s):  
J. CRUICKSHANK ◽  
A. HERMAN ◽  
R. QUINLAN ◽  
F. SZECHTMAN
Keyword(s):  
Local Ring ◽  
Unitary Group ◽  
Quadratic Extension ◽  
Unitary Groups ◽  
Weil Representation ◽  
Local Rings ◽  
Hermitian Forms ◽  
Finite Local Ring

We study hermitian forms and unitary groups defined over a local ring, not necessarily commutative, equipped with an involution. When the ring is finite we obtain formulae for the order of the unitary groups as well as their point stabilizers, and use these to compute the degrees of the irreducible constituents of the Weil representation of a unitary group associated to a ramified quadratic extension of a finite local ring.

Normal structure of the unitary group over a local ring

1984 ◽  
Vol 27 (4) ◽  
pp. 2944-2954 ◽  
Author(s):  
S. L. Krupetskii
Keyword(s):  
Local Ring ◽  
Unitary Group ◽  
Normal Structure

scholarly journals LOCAL BORCHERDS PRODUCTS FOR UNITARY GROUPS

2017 ◽  
Vol 234 ◽  
pp. 139-169
Author(s):  
ERIC HOFMANN
Keyword(s):  
Boundary Component ◽  
Unitary Group ◽  
Picard Group ◽  
Unitary Groups ◽  
Weil Representation ◽  
Cusp Forms ◽  
Modular Variety ◽  
Arithmetic Subgroup ◽  
Torsion Element ◽  
Vector Valued

For the modular variety attached to an arithmetic subgroup of an indefinite unitary group of signature $(1,n+1)$, with $n\geqslant 1$, we study Heegner divisors in the local Picard group over a boundary component of a compactification. For this purpose, we introduce local Borcherds products. We obtain a precise criterion for local Heegner divisors to be torsion elements in the Picard group, and further, as an application, we show that the obstructions to a local Heegner divisor being a torsion element can be described by certain spaces of vector-valued elliptic cusp forms, transforming under a Weil representation.

Artinian Local Rings Whose Annihilating-ideal Graphs Are Star Graphs

2015 ◽  
Vol 22 (01) ◽  
pp. 73-82 ◽  
Author(s):  
Houyi Yu ◽  
Tongsuo Wu ◽  
Weiping Gu
Keyword(s):  
Local Ring ◽  
Complete Characterization ◽  
Local Rings ◽  
Star Graph ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Star Graphs ◽  
Finite Local Ring ◽  
Necessary And Sufficient

In this paper, a necessary and sufficient condition is given for a commutative Artinian local ring whose annihilating-ideal graph is a star graph. Also, a complete characterization is established for a finite local ring whose annihilating-ideal graph is a star graph.

CONGRUENCE OF SYMMETRIC INNER PRODUCTS OVER FINITE COMMUTATIVE RINGS OF ODD CHARACTERISTIC

2017 ◽  
Vol 96 (3) ◽  
pp. 389-397
Author(s):  
SONGPON SRIWONGSA
Keyword(s):  
Commutative Ring ◽  
Local Ring ◽  
Finite Rank ◽  
Congruence Class ◽  
Commutative Rings ◽  
Inner Products ◽  
Finite Local Ring ◽  
Finite Commutative Ring ◽  
Finite Commutative Rings

Let $R$ be a finite commutative ring of odd characteristic and let $V$ be a free $R$-module of finite rank. We classify symmetric inner products defined on $V$ up to congruence and find the number of such symmetric inner products. Additionally, if $R$ is a finite local ring, the number of congruent symmetric inner products defined on $V$ in each congruence class is determined.

On the Tempered Spectrum of Quasi-Split Classical Groups II

2001 ◽  
Vol 53 (2) ◽  
pp. 244-277 ◽  
Author(s):  
David Goldberg ◽  
Freydoon Shahidi
Keyword(s):  
Parabolic Subgroup ◽  
Characteristic Zero ◽  
Unitary Group ◽  
Quadratic Extension ◽  
Intertwining Operators ◽  
Classical Groups ◽  
Maximal Parabolic Subgroup ◽  
Supercuspidal Representation

AbstractWe determine the poles of the standard intertwining operators for a maximal parabolic subgroup of the quasi-split unitary group defined by a quadratic extension E/F of p-adic fields of characteristic zero. We study the case where the Levi component M ≃ GLn(E) × Um(F), with n ≡ m (mod 2). This, along with earlier work, determines the poles of the local Rankin-Selberg product L-function L(s, t′ × τ), with t′ an irreducible unitary supercuspidal representation of GLn(E) and τ a generic irreducible unitary supercuspidal representation of Um(F). The results are interpreted using the theory of twisted endoscopy.

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