On the geometry of varieties of invertible symmetric and skew-symmetric matrices

Oliver Jones

Vol. 180 (1997), No. 1, 89–100

DOI: 10.2140/pjm.1997.180.89

Abstract

Let Sym(n,F) and Sk(n,F) denote the algebraic varieties of n × n invertible symmetric and skew-symmetric matrices over a field F, respectively. We first show how the homotopy type of Sym(n,R) and the homology groups of Sk(n,R) can be determined using an alternative method to Iwasawa decomposition. Then, using recent results of Dimca and Lehrer, the weight polynomials of Sym(n,C) and Sk(n,C) are calculated.

Milestones

Received: 21 April 1995

Revised: 6 September 1995

Published: 1 September 1997