On the isospectra and the isometries of the Aloff-Wallach spaces
Bull. Korean Math. Soc. 2001 Vol. 38, No. 2, 413-425
Dosang Joe, Yoonweon Lee, Jinsung Park, and Jeong Seog Ryu
Ewha Woman's University, Inha University, Korea Institute for Advanced Study, Hongik University
Abstract : We use the branching rules on $SU(3)$ to show that if two Aloff-Wallach spaces $M_{k,l}$ and $M_{k',l'}$ are isospectral for the Laplacian acting on smooth functions, they are isometric. We also show that $1$ is the non-zero smallest eigenvalue among all Aloff-Wallach spaces and compute the multiplicities.
Keywords : Aloff-Wallach space, Laplacian, Casimir operator, branching rules
MSC numbers : 22E15, 58G40
Downloads: Full-text PDF  

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd