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 computed in terms of the dimensions of the eigenspaces of L.
Acknowledgements
R. Durán Díaz and J. Muñoz Masqué are supported by Ministerio de Educación y Ciencia (Spain) under grant MTM2005-00173, and L. Hernández Encinas and Seok-Zun Song are supported by Korean Science and Engineering Foundation (Korea) under grant F01-2007-000-10047-0.