Global representations of the conformal group and eigenspaces of the Yamabe operator on S1 × Sn
Document Type
Article
Publication Date
1-1-2015
Abstract
Using parabolic induction, a global representation of a double cover of the conformal group SO(2, n + 1)0 is constructed. Its space of finite vectors is realized as a direct sum of eigenspaces of the Yamabe operator on S1 × Sn. The explicit form of the corresponding eigenvalues is obtained. An explicit basis of K-finite eigenvectors is used to study its structure as a representation of the Lie algebra of the conformal group.
Publication Title
Pacific Journal of Mathematics
Volume
275
Issue
2
First Page
463
Last Page
480
Digital Object Identifier (DOI)
10.2140/pjm.2015.275.463
ISSN
00308730
E-ISSN
19455844
Citation Information
Sepanski, & Franco, J. (2015). Global representations of the conformal group and eigenspaces of the Yamabe operator onS1×Sn. Pacific Journal of Mathematics, 275(2), 463–480. https://doi.org/10.2140/pjm.2015.275.463
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