Discrete components of some complementary series
-
Birgit Speh
and
T. N. Venkataramana
Abstract
We show that complementary series representations of SO(n, 1), which are sufficiently close to a cohomological representation contain discretely, complementary series of SO(m, 1) also sufficiently close to cohomological representations, provided that the degree of the cohomological representation does not exceed m/2.
We prove, as a consequence, that the cohomological representation of degree i of the group SO(n, 1) contains discretely, the cohomological representation of degree i of the subgroup SO(m, 1) if i ≤ m/2.
As a global application, we show that if G/ℚ is a semisimple algebraic group such that G(ℝ) = SO(n, 1) up to compact factors, and if we assume that for all n, the tempered cohomological representations are not limits of complementary series in the automorphic dual of SO(n, 1), then for all n, non-tempered cohomological representations are isolated in the automorphic dual of G. This reduces conjectures of Bergeron to the case of tempered cohomological representations.
© de Gruyter 2011
Articles in the same Issue
- Almost global existence for quasilinear wave equations with inhomogeneous terms in 3D
- Heegner points and Eisenstein series
- Discrete components of some complementary series
- Even universal binary Hermitian lattices over imaginary quadratic fields
- Combinatorial classification of piecewise hereditary algebras
- Weighted energy estimates for wave equations in exterior domains
- Invariant sets and ergodic decomposition of local semi-Dirichlet forms
- Regularity in parabolic Dini continuous systems
- The reciprocity law for the twisted second moment of Dirichlet L-functions
Articles in the same Issue
- Almost global existence for quasilinear wave equations with inhomogeneous terms in 3D
- Heegner points and Eisenstein series
- Discrete components of some complementary series
- Even universal binary Hermitian lattices over imaginary quadratic fields
- Combinatorial classification of piecewise hereditary algebras
- Weighted energy estimates for wave equations in exterior domains
- Invariant sets and ergodic decomposition of local semi-Dirichlet forms
- Regularity in parabolic Dini continuous systems
- The reciprocity law for the twisted second moment of Dirichlet L-functions
