Tempered Homogeneous Spaces III
Copyright policy )Tempered Homogeneous Spaces III
AbstractLet G be a complex semisimple Lie group and H a complex closed connected subgroup. Let and be their Lie algebras. We prove that the regular representation of G in $L^2(G/H)$ is tempered if and only if the orthogonal of in contains regular elements by showing simultaneously the equivalence to other striking conditions, such as has a solvable limit algebra.
- French National Centre for Scientific Research France
- University of Paris-Saclay France
- Département de Mathématiques France
- University of Tokyo Japan
- University of Paris-Sud France
tempered representations, tempered unitary representations, Lie groups, homogeneous spaces, Primary 22E46, Secondary 43A85, 22F30, symmetric spaces, matrix coefficients, Group Theory (math.GR), Homogeneous spaces, unitary representations, Harmonic analysis on homogeneous spaces, Semisimple Lie groups and their representations, Lie algebras, FOS: Mathematics, Representation Theory (math.RT), Mathematics - Group Theory, Representations of Lie and linear algebraic groups over real fields: analytic methods, Mathematics - Representation Theory
tempered representations, tempered unitary representations, Lie groups, homogeneous spaces, Primary 22E46, Secondary 43A85, 22F30, symmetric spaces, matrix coefficients, Group Theory (math.GR), Homogeneous spaces, unitary representations, Harmonic analysis on homogeneous spaces, Semisimple Lie groups and their representations, Lie algebras, FOS: Mathematics, Representation Theory (math.RT), Mathematics - Group Theory, Representations of Lie and linear algebraic groups over real fields: analytic methods, Mathematics - Representation Theory
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