Lattice action on the boundary of SL(n,R)

Alexander Gorodnik (Gorodnyk)

doi:10.1017/S0143385703000154

Lattice action on the boundary of SL(n,R)

Alexander Gorodnik (Gorodnyk)

Research output: Contribution to journal › Article (Academic Journal) › peer-review

13 Citations (Scopus)

Abstract

Let Gamma be a lattice in G = SL(n, R) and X = G/S be a homogeneous space of G, where S is a closed subgroup of G which contains a real algebraic subgroup H such that G/H is compact. We establish the uniform distribution of orbits of Gamma in X analogous to the classical equidistribution on a torus. To obtain this result, we first prove an ergodic theorem along balls in the connected component of a Borel subgroup of G.

Translated title of the contribution	Lattice action on the boundary of SL(n,R)
Original language	English
Pages (from-to)	1817-1837
Number of pages	21
Journal	Ergodic Theory and Dynamical Systems
Volume	23
Issue number	6
DOIs	https://doi.org/10.1017/S0143385703000154
Publication status	Published - Dec 2003

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Publisher: Cambridge Univ Press

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10.1017/S0143385703000154

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title = "Lattice action on the boundary of SL(n,R)",

abstract = "Let Gamma be a lattice in G = SL(n, R) and X = G/S be a homogeneous space of G, where S is a closed subgroup of G which contains a real algebraic subgroup H such that G/H is compact. We establish the uniform distribution of orbits of Gamma in X analogous to the classical equidistribution on a torus. To obtain this result, we first prove an ergodic theorem along balls in the connected component of a Borel subgroup of G.",

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TY - JOUR

T1 - Lattice action on the boundary of SL(n,R)

AU - Gorodnik (Gorodnyk), Alexander

N1 - Publisher: Cambridge Univ Press

PY - 2003/12

Y1 - 2003/12

N2 - Let Gamma be a lattice in G = SL(n, R) and X = G/S be a homogeneous space of G, where S is a closed subgroup of G which contains a real algebraic subgroup H such that G/H is compact. We establish the uniform distribution of orbits of Gamma in X analogous to the classical equidistribution on a torus. To obtain this result, we first prove an ergodic theorem along balls in the connected component of a Borel subgroup of G.

AB - Let Gamma be a lattice in G = SL(n, R) and X = G/S be a homogeneous space of G, where S is a closed subgroup of G which contains a real algebraic subgroup H such that G/H is compact. We establish the uniform distribution of orbits of Gamma in X analogous to the classical equidistribution on a torus. To obtain this result, we first prove an ergodic theorem along balls in the connected component of a Borel subgroup of G.

U2 - 10.1017/S0143385703000154

DO - 10.1017/S0143385703000154

M3 - Article (Academic Journal)

SN - 0143-3857

VL - 23

SP - 1817

EP - 1837

JO - Ergodic Theory and Dynamical Systems

JF - Ergodic Theory and Dynamical Systems

IS - 6

ER -

Lattice action on the boundary of SL(n,R)

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