The spectrum of the Laplace operator on connected compact simple rank three Lie groups

TL;DR

This paper explicitly calculates the Laplace operator spectrum on all connected compact simple rank three Lie groups with biinvariant metrics, linking the results to number theory and quadratic forms.

Contribution

It provides explicit formulas for the spectrum of the Laplace operator on rank three Lie groups and connects these results to number theory and quadratic forms.

Findings

Explicit spectrum formulas for all rank three Lie groups

Connection established between spectra and number theory

Insights into quadratic forms related to the spectra

Abstract

In this paper are given explicit calculations of Laplace operator spectrum for smooth real/complex-valued functions on all connected compact simple rank three Lie groups with biinvariant Riemannian metric and established a connection of obtained formulas with the number theory and integer ternary and binary quadratic forms.