We show that joinings of higher rank torus actions on -arithmetic quotients of semi-simple or perfect algebraic groups must be algebraic.
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DOI : 10.1007/s10240-019-00103-y
Einsiedler, Manfred 1 ; Lindenstrauss, Elon 1
@article{PMIHES_2019__129__83_0,
author = {Einsiedler, Manfred and Lindenstrauss, Elon},
title = {Joinings of higher rank torus actions on homogeneous spaces},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {83--127},
year = {2019},
publisher = {Springer Berlin Heidelberg},
address = {Berlin/Heidelberg},
volume = {129},
doi = {10.1007/s10240-019-00103-y},
mrnumber = {3949028},
zbl = {1423.22014},
language = {en},
url = {https://www.numdam.org/articles/10.1007/s10240-019-00103-y/}
}
TY - JOUR AU - Einsiedler, Manfred AU - Lindenstrauss, Elon TI - Joinings of higher rank torus actions on homogeneous spaces JO - Publications Mathématiques de l'IHÉS PY - 2019 SP - 83 EP - 127 VL - 129 PB - Springer Berlin Heidelberg PP - Berlin/Heidelberg UR - https://www.numdam.org/articles/10.1007/s10240-019-00103-y/ DO - 10.1007/s10240-019-00103-y LA - en ID - PMIHES_2019__129__83_0 ER -
%0 Journal Article %A Einsiedler, Manfred %A Lindenstrauss, Elon %T Joinings of higher rank torus actions on homogeneous spaces %J Publications Mathématiques de l'IHÉS %D 2019 %P 83-127 %V 129 %I Springer Berlin Heidelberg %C Berlin/Heidelberg %U https://www.numdam.org/articles/10.1007/s10240-019-00103-y/ %R 10.1007/s10240-019-00103-y %G en %F PMIHES_2019__129__83_0
Einsiedler, Manfred; Lindenstrauss, Elon. Joinings of higher rank torus actions on homogeneous spaces. Publications Mathématiques de l'IHÉS, Tome 129 (2019), pp. 83-127. doi: 10.1007/s10240-019-00103-y
[1.] Integer points on spheres and their orthogonal lattices, Invent. Math., Volume 206 (2016), pp. 379-396 | MR | Zbl | DOI
[2.] Some finiteness properties of adele groups over number fields, Publ. Math. IHES., Volume 16 (1963), pp. 5-30 | MR | Zbl | Numdam | DOI
[3.] Hyperbolic distribution problems and half-integral weight Maass forms, Invent. Math., Volume 92 (1988), pp. 73-90 | MR | DOI | Zbl
[4.] Invariant measures on for split simple Lie groups , Commun. Pure Appl. Math., Volume 56 (2003), pp. 1184-1221 (Dedicated to the memory of Jürgen K. Moser) | MR | DOI | Zbl
[5.] Rigidity of measures—the high entropy case, and non-commuting foliations, probability in mathematics, Isr. J. Math., Volume 148 (2005), pp. 169-238 | Zbl | MR | DOI
[6.] Diagonalizable flows on locally homogeneous spaces and number theory, International Congress of Mathematicians, vol. II, Eur. Math. Soc., Zürich, 2006, pp. 1731-1759 | MR | Zbl
[7.] Joinings of higher-rank diagonalizable actions on locally homogeneous spaces, Duke Math. J., Volume 138 (2007), pp. 203-232 | MR | DOI | Zbl
[8.] On measures invariant under diagonalizable actions: the rank-one case and the general low-entropy method, J. Mod. Dyn., Volume 2 (2008), pp. 83-128 | MR | Zbl | DOI
[9.] Diagonal actions on locally homogeneous spaces, Homogeneous Flows, Moduli Spaces and Arithmetic, 10, Am. Math. Soc., Providence, 2010, pp. 155-241 | MR | Zbl
[10.] On measures invariant under tori on quotients of semisimple groups, Ann. Math. (2), Volume 181 (2015), pp. 993-1031 | MR | DOI | Zbl
[11.] A joinings classification and a special case of Raghunathan’s conjecture in positive characteristic, J. Anal. Math., Volume 116 (2012), pp. 299-334 (with an appendix by Kevin Wortman) | MR | DOI | Zbl
[12.] Invariant measures and the set of exceptions to Littlewood’s conjecture, Ann. Math., Volume 164 (2006), pp. 513-560 | MR | DOI | Zbl
[13.] Distribution of periodic torus orbits and Duke’s theorem for cubic fields, Ann. Math., Volume 173 (2011), pp. 815-885 | MR | DOI | Zbl
[14.] Unipotent flows and counting lattice points on homogeneous varieties, Ann. Math. (2), Volume 143 (1996), pp. 253-299 | MR | DOI | Zbl
[15.] Non-divergence of translates of certain algebraic measures, Geom. Funct. Anal., Volume 7 (1997), pp. 48-80 | MR | DOI | Zbl
[16.] Disjointness in ergodic theory, minimal sets, and a problem in Diophantine approximation, Math. Syst. Theory, Volume 1 (1967), pp. 1-49 | MR | DOI | Zbl
[17.] The subconvexity problem for Rankin-Selberg -functions and equidistribution of Heegner points. II, Invent. Math., Volume 163 (2006), pp. 581-655 | MR | DOI | Zbl
[18.] Some ergodic properties of commuting diffeomorphisms, Ergod. Theory Dyn. Syst., Volume 13 (1993), pp. 73-100 | MR | DOI | Zbl
[19.] Invariant measures for higher-rank hyperbolic Abelian actions, Ergod. Theory Dyn. Syst., Volume 16 (1996), pp. 751-778 | MR | DOI | Zbl
[20.] Invariant measures and arithmetic quantum unique ergodicity, Ann. Math. (2), Volume 163 (2006), pp. 165-219 | MR | DOI | Zbl
[21.] Ergodic Properties of Algebraic Fields, 45, Springer New York Inc., New York, 1968 (Translated from the Russian by, Keane, M. S.) | Zbl | MR | DOI
[22.] Discrete Subgroups of Semisimple Lie Groups, 17, Springer, Berlin, 1991 (x+388 pp.) | Zbl | MR | DOI
[23.] Problems and conjectures in rigidity theory, Mathematics: Frontiers and Perspectives, Am. Math. Soc., Providence, 2000, pp. 161-174 | MR | Zbl
[24.] Invariant measures for actions of unipotent groups over local fields on homogeneous spaces, Invent. Math., Volume 116 (1994), pp. 347-392 | MR | DOI | Zbl
[25.] Measure rigidity for almost linear groups and its applications, J. Anal. Math., Volume 69 (1996), pp. 25-54 | MR | DOI | Zbl
[26.] Topics in Ergodic Theory, 75, Cambridge University Press, Cambridge/New York, 1981 | Zbl | MR
[27.] Horocycle flows, joinings and rigidity of products, Ann. Math., Volume 118 (1983), pp. 277-313 | MR | DOI | Zbl
[28.] On measure rigidity of unipotent subgroups of semisimple groups, Acta Math., Volume 165 (1990), pp. 229-309 | MR | DOI | Zbl
[29.] On Raghunathan’s measure conjecture, Ann. Math., Volume 134 (1991), pp. 545-607 | MR | DOI | Zbl
[30.] Raghunathan’s conjectures for Cartesian products of real and p-adic Lie groups, Duke Math. J., Volume 77 (1995), pp. 275-382 | MR | DOI | Zbl
[31.] and invariant measures and entropy, Ergod. Theory Dyn. Syst., Volume 10 (1990), pp. 395-406 | MR | Zbl | DOI
[32.] Limit distributions of expanding translates of certain orbits on homogeneous spaces, Proc. Indian Acad. Sci. Math. Sci., Volume 106 (1996), pp. 105-125 | MR | DOI | Zbl
[33.] Linear Algebraic Groups, Birkhäuser Boston, Boston, 1998 | Zbl | MR | DOI
[34.] Reductive groups over local fields, Proc. Symp. Pure Math., Volume 33 (1979), pp. 29-69 | MR | DOI | Zbl
[35.] Orbits on homogeneous spaces of arithmetic origin and approximations, Analysis on Homogeneous Spaces and Representation Theory of Lie Groups, Okayama–Kyoto, 26, Math. Soc. Japan, Tokyo, 1997, pp. 265-297 (2000) | MR | Zbl
[36.] Rigidity of horospherical foliations, Ergod. Theory Dyn. Syst., Volume 9 (1989), pp. 191-205 | MR | DOI | Zbl
[37.] R. Zhang, The associated Dirichlet series1, arXiv.
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