IJPAM: Volume 87, No. 4 (2013)

THE LAPLACIAN ON HOMOGENEOUS SPECIAL
ORTHOGONAL SPACES AND THE INVERSE
BRANCHING RULE

Liangzhong Hu$^1$, José João Rossetto$^2$
$^{1,2}$Department of Mathematics
Federal University of Paraná
C.P. 019081, Curitiba, PR, 81531-990, BRAZIL


Abstract. The solution of the eigenvalue problem of the Laplacian with the normal metric induced by the Killing form on homogeneous special orthogonal spaces $SO(2n+1)/SO(2n)$ is given. The corresponding inverse branching rule from $SO(2n)$ to $SO(2n+1)$ is obtained.

Received: June 30, 2013

AMS Subject Classification: 17B20, 22E46, 43A85, 81R05

Key Words and Phrases: Laplacian, homogeneous space, Casimir element, highest weight, branching rule

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DOI: 10.12732/ijpam.v87i4.11 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 87
Issue: 4