Tempered subgroups and representations with minimal decay of matrix coefficients

DOI10.24033/bsmf.2329zbMath0917.22008OpenAlexW158095931MaRDI QIDQ4239812

Hee Oh

Publication date: 13 July 1999

Published in: Bulletin de la Société mathématique de France (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=BSMF_1998__126_3_355_0

zbMATH Keywords

unitary representationmatrix coefficientcompact quotientsimple real Lie grouptempered subgroup

Mathematics Subject Classification ID

Differential geometry of homogeneous manifolds (53C30) Semisimple Lie groups and their representations (22E46) Discrete subgroups of Lie groups (22E40) Discontinuous groups of transformations (57S30)

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A cohomological obstruction to the existence of compact Clifford-Klein forms ⋮ Best possible rates of distribution of dense lattice orbits in homogeneous spaces ⋮ Semisimple symmetric spaces that do not model any compact manifold ⋮ Quantitative multiple mixing ⋮ Pointwise equidistribution for one parameter diagonalizable group action on homogeneous space ⋮ Random walks, spectral gaps, and Khintchine's theorem on fractals ⋮ Higher Order Correlations for Group Actions ⋮ Existence of compact quotients of homogeneous spaces, measurably proper actions, and decay of matrix coefficients ⋮ Quantitative ergodic theorems and their number-theoretic applications ⋮ Almost-prime times in horospherical flows on the space of lattices ⋮ A quantitative Oppenheim theorem for generic ternary quadratic forms ⋮ Geometric invariants of locally symmetric spaces and multiplier theorems ⋮ Explicit Kazhdan constants for representations of semisimple and arithmetic groups ⋮ Analogs of Wiener's ergodic theorems for semisimple Lie groups. II ⋮ Shrinking target problems for flows on homogeneous spaces ⋮ Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants ⋮ Semisimple subalgebras in simple Lie algebras and a computational approach to the compact Clifford–Klein forms problem ⋮ Exotic group \(C^*\)-algebras of simple Lie groups with real rank one

Cites Work

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• Non-Abelian harmonic analysis. Applications of \(SL(2,{\mathbb{R}})\)
• Lie groups and Lie algebras III. Structure of Lie groups and Lie algebras. Transl. from the Russian by V. Minachin
• On the decay of matrix coefficients for exceptional groups
• Groupes reductifs
• Canonical Semi-Invariants and the Plancherel Formula for Parabolic Groups
• Existence of compact quotients of homogeneous spaces, measurably proper actions, and decay of matrix coefficients

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