Vol. 275, No. 2, 2015

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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

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.

globalizations, Yamabe operator, conformal Laplace operator, Lie group, conformal group, parabolic induction
Mathematical Subject Classification 2010
Primary: 22E46, 22E70
Received: 8 July 2014
Revised: 10 November 2014
Accepted: 13 November 2014
Published: 15 May 2015
Mark R. Sepanski
Department of Mathematics
Baylor University
One Bear Place #97328
Waco, TX 76798-7328
United States
Jose A. Franco
Department of Mathematics and Statistics
University of North Florida
1 UNF Drive
Jacksonville, FL 32224
United States