THE SPECTRUM OF THE LAPLACE OPERATOR ON THE MANIFOLD Sp(n)/Sp(q) X Sp(n-q)

Fida El Chami (1)

1 LU / ULB - الجامعة اللبنانية [بيروت] = Lebanese University [Beirut] = Université libanaise [Beyrouth]

In this paper, we compute the Laplace spectrum on the forms of the manifold Sp(n)/Sp(q) XSp(n-q). The method is based on the representation theory of compact Lie groups and the ”identification” of the Laplace operator with the Casimir operator in symmetric spaces.

Mots clés: Laplace spectrum; Differential forms; Representation theory; Casimir operator.; Casimir operator

Domaines: Géométrie différentielle [math.DG]

Fida El Chami. THE SPECTRUM OF THE LAPLACE OPERATOR ON THE MANIFOLD Sp(n)/Sp(q) X Sp(n-q). 2011. ⟨hal-00577922⟩