This article is cited in 5 papers

The Laplace Operator Spectrum on Compact Simply Connected Rank Two Lie Groups

V. N. Berestovskii, V. M. Svirkin

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science

Abstract: In the paper, we suggest an algorithm for calculation of the Laplace operator spectrum for real-valued functions defined on a compact simply connected simple Lie group with a bi-invariant Riemannian metric and establish a connection of the Ricci curvature of this metric with the spectrum. By means of the algorithm suggested and with the use of results of the number theory and the theory of integral binary quadratic forms, an explicit calculation of the spectrum for all compact simply connected simple Lie groups of rank two is given.

Keywords: Laplace operator, spectrum, group representation, Killing form, Ricci curvature.

UDC: 514.764.227+514.765+517.984.56+511

Received: 12.08.2009