#### Vol. 275, No. 2, 2015

 Recent Issues Vol. 298: 1 Vol. 297: 1  2 Vol. 296: 1  2 Vol. 295: 1  2 Vol. 294: 1  2 Vol. 293: 1  2 Vol. 292: 1  2 Vol. 291: 1  2 Online Archive Volume: Issue:
 The Journal Subscriptions Editorial Board Officers Special Issues Submission Guidelines Submission Form Contacts Author Index To Appear ISSN: 0030-8730 Other MSP Journals
Global representations of the conformal group and eigenspaces of the Yamabe operator on $S^1 \times S^n$

### Mark R. Sepanski and Jose A. Franco

Vol. 275 (2015), No. 2, 463–480
##### Abstract

Using parabolic induction, a global representation of a double cover of the conformal group $SO{\left(2,n+1\right)}_{0}$ is constructed. Its space of finite vectors is realized as a direct sum of eigenspaces of the Yamabe operator on ${S}^{1}×{S}^{n}$. 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.

##### Keywords
globalizations, Yamabe operator, conformal Laplace operator, Lie group, conformal group, parabolic induction
##### Mathematical Subject Classification 2010
Primary: 22E46, 22E70