A branching law from Sp(n) TO Sp(q) × Sp(n-q) and an application to laplace operator spectra

Abstract

In this paper, we give a branching law from the group Sp(n) to the subgroup Sp(q) × Sp(n-q). We propose an application of this result to compute the Laplace spectrum on the forms of the manifold Sp(n)/Sp(q)×Sp(n-q), using the “identification” of the Laplace operator with the Casimir operator in symmetric spaces.