Israel Journal of Mathematics

, Volume 195, Issue 1, pp 393–447 | Cite as

A Haar component for quantum limits on locally symmetric spaces

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Abstract

We prove lower bounds for the entropy of limit measures associated to non-degenerate sequences of eigenfunctions on locally symmetric spaces of non-positive curvature. In the case of certain compact quotients of the space of positive definite n × n matrices (any quotient for n = 3, quotients associated to inner forms in general), measure classification results then show that the limit measures must have a Haar component. This is consistent with the conjecture that the limit measures are absolutely continuous.

Keywords

Lyapunov Exponent Symmetric Space Weyl Group Quantum Limit Division Algebra 
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Copyright information

© Hebrew University Magnes Press 2013

Authors and Affiliations

  1. 1.Laboratoire de MathématiqueUniversité d’Orsay Paris XIOrsay CedexFrance
  2. 2.Department of MathematicsUniversity of British ColumbiaVancouverCanada

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