Global representations of the conformal group and eigenspaces of the Yamabe operator on S1 × Sn
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.
Pacific Journal of Mathematics
Digital Object Identifier (DOI)
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