Intersections of the space of skew-symmetric maps with its translates
Daniel B. Shapiro · Pacific Journal of Mathematics · 1978
For a quadratic space V over a field K, let 5£ C End(V) be the space of all maps which are skew-symmetric with respect to the inner product.For gGGL(V), let ®(g) = dim(i?fl g££).In this paper we determine the largest few values possible for 3)(g), and we classify the maps g which achieve these values.The restriction of this result to maps g in the orthogonal group 6(V) generalizes the characterization of ± symmetries originally proved by Botta and Pierce.