Intersections of the space of skew-symmetric maps with its translates

Daniel Byron Shapiro

Vol. 75 (1978), No. 2, 553–560

DOI: 10.2140/pjm.1978.75.553

Abstract

For a quadratic space V over a field K, let ℒ⊆ End(V ) be the space of all maps which are skew-symmetric wilh respect to the inner product. For g ∈ GL(V ), let 𝒟(g) = dim(ℒ∩gℒ). In this paper we determine the largest few values possible for 𝒟(g), and we classify the maps g which achieve these values. The restriction of this result to maps g in the orthogonal group 𝒪(V ) generalizes the characterization of ± symmetries originally proved by Botta and Pierce.

Mathematical Subject Classification 2000

Primary: 15A63

Milestones

Received: 20 March 1977

Published: 1 April 1978