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15 April 2004 Uniform distribution of orbits of lattices on spaces of frames
Alexander Gorodnik
Duke Math. J. 122(3): 549-589 (15 April 2004). DOI: 10.1215/S0012-7094-04-12234-1

Abstract

We study distribution of orbits of a lattice $\Gamma\subseteq\SL(n,\mathbb{R})$ in the the space $\mathcal{V}_{n,l}$ of $l$-frames in $\mathbb{R}^n$ ($1\le l\le n-1$). Examples of dense $\Gamma$-orbits are known from the work of Dani, Raghavan, and Veech. We show that dense orbits of $\Gamma$ are uniformly distributed in $\mathcal{V}_{n,l}$ with respect to an explicitly described measure. We also establish an analogous result for lattices in ${\rm Sp}(n,\mathbb{R})$ which act on the space of isotropic $n$-frames.

Citation

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Alexander Gorodnik. "Uniform distribution of orbits of lattices on spaces of frames." Duke Math. J. 122 (3) 549 - 589, 15 April 2004. https://doi.org/10.1215/S0012-7094-04-12234-1

Information

Published: 15 April 2004
First available in Project Euclid: 22 April 2004

zbMATH: 1067.37004
MathSciNet: MR2057018
Digital Object Identifier: 10.1215/S0012-7094-04-12234-1

Subjects:
Primary: 37A15 22E40 37A17 20H05

Rights: Copyright © 2004 Duke University Press

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Vol.122 • No. 3 • 15 April 2004
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