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Hyperbolic spaces, principal series and ${\rm O}(2,\infty)$
- Source :
- Archiv der Mathematik, vol. 114, No. 1 (2020)
- Publication Year :
- 2018
-
Abstract
- We prove that there exists no irreducible representation of the identity component of the isometry group ${\rm PO}(1,n)$ of the real hyperbolic space of dimension $n$ into the group ${\rm O}(2,\infty)$, if $n\geq 3$. This is motivated by the existence of irreducible representations (arising from the spherical principal series) of ${\rm PO}(1,n)^{\circ}$ into the groups ${\rm O}(p,\infty)$ for other values of $p$.<br />Comment: 8 pages
- Subjects :
- Mathematics - Group Theory
Mathematics - Representation Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- Archiv der Mathematik, vol. 114, No. 1 (2020)
- Publication Type :
- Report
- Accession number :
- edsarx.1812.03782
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s00013-019-01399-2