Spectral uniqueness of bi-invariant metrics on symplectic groups

Abstract

In this short note, we prove that a bi-invariant Riemannian metric on $\mathrm{Sp}(n)$ is uniquely determined by the spectrum of its Laplace-Beltrami operator within the class of left-invariant metrics on $\mathrm{Sp}(n)$. In other words, on any of these compact simple Lie groups, every left-invariant metric which is not right-invariant cannot be isospectral to a bi-invariant metric. The proof is elementary and uses a very strong spectral obstruction proved by Gordon, Schueth, and Sutton.

The proof of Lemma 3.1 was modified

References in corpus (2)

• Spectral isolation of naturally reductive metrics on simple Lie groups
• The smallest Laplace eigenvalue of homogeneous 3-spheres

Cited by in corpus (3)

• The smallest Laplace eigenvalue of homogeneous 3-spheres
• The first eigenvalue of a homogeneous CROSS
• Spectrally distinguishing symmetric spaces I