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Equidistribution of Rational Matrices in their Conjugacy Classes

Benoist, Yves and Oh, Hee (2007) Equidistribution of Rational Matrices in their Conjugacy Classes. Geometric and Functional Analysis, 17 (1). pp. 1-32. ISSN 1016-443X. doi:10.1007/s00039-006-0585-4.

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Let G be a connected simply connected almost ℚ-simple algebraic group with G: = G(ℝ) non-compact and Γ ⊂ G_ℚ a cocompact congruence subgroup. For any homogeneous manifold x_0H ⊂ Γ∖G of finite volume, and a a ∈ G_ℚ, we show that the Hecke orbit Ta(x_0H) is equidistributed on Γ∖G as deg(a) → ∞, provided H is a non-compact commutative reductive subgroup of G. As a corollary, we generalize the equidistribution result of Hecke points ([COU], [EO_1]) to homogeneous spaces G/H. As a concrete application, we describe the equidistribution result in the rational matrices with a given characteristic polynomial.

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Additional Information:© 2007 Birkhäuser Verlag, Basel. Received: May 2005. Revision: March 2006. Accepted: June 2006. ONLINE FIRST: November 2006. The second author partially supported by DMS 0333397. We would like to thank Elon Lindenstrauss for useful discussions. The first named author would like to thank Caltech where most of the collaboration took place.
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Subject Keywords:Equidistribution, conjugacy classes, Hecke operators, rational matrices, Hecke points
Issue or Number:1
Classification Code:AMS Mathematics Subject Classification: 11D45, 37A17, 37A25, 37A45
Record Number:CaltechAUTHORS:20170408-141923523
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Official Citation:Benoist, Y. & Oh, H. GAFA, Geom. funct. anal. (2007) 17: 1. doi:10.1007/s00039-006-0585-4
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:75923
Deposited By: 1Science Import
Deposited On:20 Apr 2017 21:21
Last Modified:15 Nov 2021 16:56

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