Invariant theory of special orthogonal groups

Helmer Aslaksen, Eng-Chye Tan and Chen-Bo Zhu

Vol. 168 (1995), No. 2, 207–215

DOI: 10.2140/pjm.1995.168.207

Abstract

In this paper we study the action of SO(n) on m-tuples of n×n matrices by simultaneous conjugation. We show that the polynomial invariants are generated by traces and polarized Pfaffians of skewsymmetric projections. We also discuss the same problem for other classical groups.

Mathematical Subject Classification 2000

Primary: 13A50

Secondary: 15A15, 15A72, 16R30, 20G05

Milestones

Received: 10 November 1992

Revised: 14 April 1993

Published: 1 April 1995