Back to Search
Start Over
A note about the generic irreducibility of the spectrum of the Laplacian on homogeneous spaces.
- Source :
- Manuscripta Mathematica; Sep2024, Vol. 175 Issue 1/2, p143-154, 12p
- Publication Year :
- 2024
-
Abstract
- Petrecca and Röser (Mathematische Zeitschrift 291:395–419, 2018) and Schueth (Ann Global Anal Geom 52:187–200, 2017) had shown that for a generic G-invariant metric g on certain compact homogeneous spaces M = G / K (including symmetric spaces of rank 1 and some Lie groups), the spectrum of the Laplace-Beltrami operator Δ g was real G-simple. The same is not true for the complex version of Δ g when there is a presence of representations of complex or quaternionic type. We show that these types of representations induces a Q 8 -action that commutes with the Laplacian in such way that G-properties of the real version of the operator have to be understood as (Q 8 × G) -properties on its corresponding complex version. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00252611
- Volume :
- 175
- Issue :
- 1/2
- Database :
- Complementary Index
- Journal :
- Manuscripta Mathematica
- Publication Type :
- Academic Journal
- Accession number :
- 179234790
- Full Text :
- https://doi.org/10.1007/s00229-024-01567-x