Vortrag: "The spectrum of the Laplacian on the 5-sphere"

Abstract:

We determine the spectrum of the Laplacian on the 5-sphere using representation theory of Lie groups. For this we realize the sphere as a compact homogeneous space and determine the irreducible representations which enter into its Peter-Weyl decomposition using branching laws for unitary groups. Via Weyl's unitary trick this ultimately amounts to study branching for GL_3(\)-representations over GL_2(\C).