Unitary groups over local rings

J. Cruickshank; A. Herman; Rachel Quinlan; Fernando Szechtman

doi:10.13025/25561

Unitary groups over local rings

J. Cruickshank
, A. Herman
, Rachel Quinlan
, Fernando Szechtman

Mathematics

University of Regina

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

4 Citations (Scopus)

Abstract

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.

Original language	English (Ireland)
Article number	1350093
Journal	Journal Of Algebra And Its Applications
Volume	13
Issue number	2
DOIs	https://doi.org/10.13025/25561 https://doi.org/10.1142/s021949881350093x
Publication status	Published - 1 Mar 2014

Keywords

Hermitian form
involution
local ring
ramified and unramified extension
unitary group

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10.13025/25561Licence: CC BY-NC-ND
10.1142/s021949881350093x

Cite this

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AU - Cruickshank, J.

AU - Herman, A.

AU - Quinlan, Rachel

AU - Szechtman, Fernando

PY - 2014/3/1

Y1 - 2014/3/1

N2 - 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.

AB - 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.

KW - Hermitian form

KW - involution

KW - local ring

KW - ramified and unramified extension

KW - unitary group

UR - http://hdl.handle.net/10379/10965

UR - https://www.scopus.com/pages/publications/84887387049

U2 - 10.13025/25561

DO - 10.13025/25561

M3 - Article

VL - 13

JO - Journal Of Algebra And Its Applications

JF - Journal Of Algebra And Its Applications

IS - 2

M1 - 1350093

ER -

Unitary groups over local rings

Abstract

Keywords

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