Dimension of the intersection of a pair of orthogonal groups
Dimension of the intersection of a pair of orthogonal groups
Abstract Let g, h:V×V→ℂ be two non-degenerate symmetric bilinear forms on a finite-dimensional complex vector space V. Let G (resp. H) be the Lie group of isometries of g (resp. h). If the endomorphism L:V→V associated to g, h is diagonalizable, then the dimension of the intersection group G∩H is …