Explicit Kazhdan constants for representations of semisimple and arithmetic groups

DOI10.5802/aif.1775zbMath0966.22004OpenAlexW2001282789MaRDI QIDQ1572634

Yehuda Shalom

Publication date: 19 July 2000

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2000__50_3_833_0

zbMATH Keywords

topological groupsemisimple groupsKazhdan constantslatticesarithmetic groupsKazhdan setproperty \((T)\)

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Unitary representations of locally compact groups (22D10) Analysis on (p)-adic Lie groups (22E35) Induced representations for locally compact groups (22D30) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

Related Items

Uniform Kazhdan constants and paradoxes of the affine plane, Towards strong Banach property (T) for \(\mathrm{SL}(3,\mathbb R)\), Recurrence and ergodicity of random walks on linear groups and on homogeneous spaces, Kazhdan constants of some colored permutation groups., Linear groups over general rings. I: Generalities., A height gap theorem for finite subsets of \(\mathrm{GL}_{d}(\overline{\mathbb{Q}})\) and nonamenable subgroups, Strong relative property \((T)\) and spectral gap of random walks, The product replacement algorithm and Kazhdan’s property (T), Acylindrically hyperbolic groups with exotic properties, Kazhdan constants for conjugacy classes of compact groups., Extreme value theory for random walks on homogeneous spaces, Uniform independence in linear groups., Measure expanding actions, expanders and warped cones, Uniform Kazhdan constant for some families of linear groups., Bounded generation and Kazhdan's property (T), The Burger-Sarnak method and operations on the unitary dual of 𝐺𝐿(𝑛), Kazhdan projections, random walks and ergodic theorems, A spectral gap property for random walks under unitary representations, KAZHDAN CONSTANTS FOR SL_n(ℤ), Kazhdan’s Property (T) via Semidefinite Optimization, Uniform nonamenability of subgroups of free Burnside groups of odd period., On convergence of random walks on moduli space, Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants, Uniform non-amenability, Dependence of Kazhdan constants on generating subsets, Exotic group \(C^*\)-algebras of simple Lie groups with real rank one

Cites Work

• Restrictions of unitary representations to lattices and associated \(C^*\)-algebras
• The unitary dual of \(Sp(n,1)\), \(n\geq 2\)
• Non-Abelian harmonic analysis. Applications of \(SL(2,{\mathbb{R}})\)
• Ramanujan duals. II
• Asymptotic properties of unitary representations
• On the spectrum of the sum of generators for a finitely generated group
• Spectral transfer and pointwise ergodic theorems for semi-simple Kazhdan groups
• Property \((T)\) and \(\widetilde{A}_ 2\) groups
• Discrete groups, expanding graphs and invariant measures. Appendix by Jonathan D. Rogawski
• On \(L^2\)-cohomology and property (T) for automorphism groups of polyhedral cell complexes
• Property (T) and Kazhdan constants for discrete groups
• Rigidity, unitary representations of semisimple groups, and fundamental groups of manifolds with rank one transformation group
• Logarithm laws for flows on homogeneous spaces
• On the decay of matrix coefficients for exceptional groups
• On problems related to growth, entropy, and spectrum in group theory
• The unitary spectrum for real rank one groups
• Connection of the dual space of a group with the structure of its closed subgroups
• Eigenvalues of the Laplacian, the first Betti number and the congruence subgroup problem
• Induced representation of locally compact groups. I
• Symmetric Random Walks on Groups
• Kazhdan constants for SL (3, Z).
• Hecke operators and distributing points on S². II
• Sharp ergodic theorems for group actions and strong ergodicity
• Growth Rates, ℤ p -Homology, and Volumes of Hyperbolic 3-Manifolds
• REPRESENTATIONS OF THE GROUPGL(n,F) WHEREFIS A NON-ARCHIMEDEAN LOCAL FIELD
• Tempered subgroups and representations with minimal decay of matrix coefficients
• Invariant measures for algebraic actions, Zariski dense subgroups and Kazhdan’s property (T)
• On uniqueness of invariant means
• Weak Containment and Induced Representations of Groups
• Ergodicity of Flows on Homogeneous Spaces
• L'algèbre de Fourier d'un groupe localement compact
• On the existence and irreducibility of certain series of representations
• Bounded generation and Kazhdan's property (T)
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