IJPAM: Volume 12, No. 4 (2004)

SPECTRA OF THE LAPLACE OPERATOR
ON GRASSMANN MANIFOLDS

Fida El Chami Department of Mathematics, Faculty of Sciences, Saint Joseph University, Campus of Sciences and Technology, B.P. 11-514, Riad El Solh, Beirut, 1107 2050, LEBANON
Department of Mathematics
Faculty of Sciences, II-Fanar
University of Lebanon
BP 90656, Jdeidet, LEBANON
e-mail: fida.sayah@fs.usj.edu.lb


Abstract.In this paper, we explicitly compute the Laplace spectrum on the forms for Grassmann manifolds. This is a generalization of A. Ikeda-Y. Taniguchi and C. Tsukamoto calculations, based on the representation theory of compact Lie groups and on the ``identification" of the Laplace operator with the Casimir operator in symmetric spaces.

Received: December 22, 2003

AMS Subject Classification: 22C05, 53C35, 58G25

Key Words and Phrases: Laplace spectrum, differential forms, representation theory, Casimir operator, Grassmann manifold

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 12
Issue: 4