Eigenspaces of the Laplacian on hyperbolic spaces: Composition series and integral transforms
Research output: Contribution to journal › Journal article › Research › peer-review
Let X be a projective real, complex, or quaternion hyperbolic space, realized as the pseudo-Riemannian symmetric space X ≅ G H with G = O(p, q), U(p, q), or Sp(p,q) (these are the classical isotropic symmetric spaces). Let Δ be the G-invariant Laplace-Beltrami operator on X. A complete description (by K-types), for each χ ∈ C, of all closed G-invariant subspaces of the eigenspace {f ∈ C∞(X)|Δf = χf} is given. The eigenspace representations are compared with principal series representations, using "Poisson-transformations". Similar results are obtained also for the exceptional isotropic symmetric space. The Langlands parameters of the spherical discrete series representations are determined.
Original language | English |
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Journal | Journal of Functional Analysis |
Volume | 70 |
Issue number | 1 |
Pages (from-to) | 194-219 |
Number of pages | 26 |
ISSN | 0022-1236 |
DOIs | |
Publication status | Published - Jan 1987 |
ID: 304299135