Measure rigidity for almost linear groups and its applications

DOI10.1007/BF02787100zbMath0864.22005OpenAlexW2073200499MaRDI QIDQ2565372

George Tomanov, Gregory A. Margulis

Publication date: 22 June 1997

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02787100

zbMATH Keywords

real Lie groupmeasure rigidity\(H\)-ergodic probability measureactions of unipotent groups on homogeneous spacesalmost linear group

Mathematics Subject Classification ID

Ergodic theory on groups (22D40) General groups of measure-preserving transformations (28D15) Discrete subgroups of Lie groups (22E40) Linear algebraic groups over local fields and their integers (20G25)

Related Items (14)

Homogeneous orbit closures and applications ⋮ Joinings of higher rank torus actions on homogeneous spaces ⋮ PROPERTY τ AND COUNTABLE BOREL EQUIVALENCE RELATIONS ⋮ Symmetry of entropy in higher rank diagonalizable actions and measure classification ⋮ Effective estimates on indefinite ternary forms ⋮ Minimality and unique ergodicity of homogeneous actions ⋮ Measure rigidity for solvable group actions in the space of lattices ⋮ Rational points on homogeneous varieties and equidistribution of adelic periods (with appendix by Mikhail Borovoi) ⋮ Rigidity of group actions on homogeneous spaces. III ⋮ Invariant measures for solvable groups and Diophantine approximation ⋮ Closures of locally divergent orbits of maximal tori and values of homogeneous forms ⋮ Distribution of periodic torus orbits on homogeneous spaces ⋮ Minimality and unique ergodicity for subgroup actions ⋮ On measures invariant under tori on quotients of semisimple groups

Cites Work

• Topological central extensions of semi-simple groups over local fields. I, II
• Raghunathan's topological conjecture and distributions of unipotent flows
• The Mautner phenomenon for general unitary representations
• On measure rigidity of unipotent subgroups of semisimple groups
• On Raghunathan's measure conjecture
• Invariant measures for actions of unipotent groups over local fields on homogeneous spaces
• Invariant measures and orbit closures for unipotent actions on homogeneous spaces
• Strict measure rigidity for unipotent subgroups of solvable groups
• Raghunathan's conjectures for Cartesian products of real and \(p\)-adic Lie groups
• Rationality properties of linear algebraic groups. II
• Measurable Quotients of Unipotent Translations on Homogeneous Spaces
• On the space of ergodic invariant measures of unipotent flows
• Values of indefinite quadratic forms at integral points and flows on spaces of lattices
• THE PROBLEM OF STRONG APPROXIMATION AND THE KNESER-TITS CONJECTURE FOR ALGEBRAIC GROUPS
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Measure rigidity for almost linear groups and its applications