On Quantum Unique Ergodicity for Locally Symmetric Spaces |
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| Authors: | Lior Silberman Akshay Venkatesh |
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| Affiliation: | (1) Department of Mathematics, Princeton University, Princeton, NJ 08544-0001, USA;(2) Present address: Department of Mathematics, Harvard University, One Oxford Street, Cambridge, MA 02138, USA;(3) Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139-4307, USA;(4) Present address: School of Mathematics, Institute for Advanced Study, One Einstein Drive, Princeton, NJ 08540, USA;(5) Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, NY 10012, USA |
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| Abstract: | ![]()
We construct an equivariant microlocal lift for locally symmetric spaces. In other words, we demonstrate how to lift, in a semi-canonical fashion, limits of eigenfunction measures on locally symmetric spaces to Cartan-invariant measures on an appropriate bundle. The construction uses elementary features of the representation theory of semisimple real Lie groups, and can be considered a generalization of Zelditch’s results from the upper half-plane to all locally symmetric spaces of noncompact type. This will be applied in a sequel to settle a version of the quantum unique ergodicity problem on certain locally symmetric spaces. The second author was supported in part by NSF Grant DMS-0245606. Part of this work was performed at the Clay Institute Mathematics Summer School in Toronto. Received: September 2005 Revision: August 2006 Accepted: August 2006 |
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| Keywords: | Automorphic forms locally symmetric spaces Lie groups quantum chaos quantum unique ergodicity microlocal lift invariant measures |
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