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On Quantum unique ergodicity for locally symmetric spaces I

Lior Silberman·Akshay Venkatesh
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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.

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BibTeXRIS

Lior Silberman, Akshay Venkatesh. 2004-07-24. On Quantum unique ergodicity for locally symmetric spaces I. https://arxiv.org/abs/math/0407413

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