Vol. 2, No. 5, 2009

Download this article
Download this article For screen
For printing
Recent Issues

Volume 10
Issue 5, 721–900
Issue 4, 541–720
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
Cover Page
Editorial Board
Editors’ Addresses
Editors’ Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Subscriptions
Editorial Login
Author Index
Coming Soon
Contacts
 
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
On the orbits of an orthogonal group action

Kyle Czarnecki, R. Michael Howe and Aaron McTavish

Vol. 2 (2009), No. 5, 495–509
Abstract

Let G be the Lie group SO(n, ) × SO(n, ) and let V be the vector space of n × n real matrices. An action of G on V is given by

(g,h).v := g1vh,(g,h) G,v V.

We consider the orbits of this group action and demonstrate a cross-section to the orbits. We then determine the stabilizer for a typical element in this cross-section and completely describe the fundamental group of an orbit of maximal dimension.

Keywords
representation theory, orbit, Lie group, homotopy group, Clifford algebra
Mathematical Subject Classification 2000
Primary: 22C05, 57S15
Secondary: 55Q52
Milestones
Received: 8 April 2008
Accepted: 28 September 2009
Published: 13 January 2010

Communicated by Józef H. Przytycki
Authors
Kyle Czarnecki
Department of Mathematics
University of Wisconsin – Parkside
900 Wood Rd.
P.O. Box 2000
Kenosha, WI 53141-2000
United States
R. Michael Howe
Department of Mathematics
University of Wisconsin – Eau Claire
508 Hibbard Humanities Hall
Eau Claire, WI 54702-4004
United States
http://www.uwec.edu/math/Faculty/howe.htm
Aaron McTavish
Department of Mathematical Sciences
University of Wisconsin – Stevens Point
Stevens Point, WI 54481-3897
United States