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
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