1 results
Quantum Unique Ergodicity on Locally Symmetric Spaces: the Degenerate Lift
-
- Journal:
- Canadian Mathematical Bulletin / Volume 58 / Issue 3 / 01 September 2015
- Published online by Cambridge University Press:
- 20 November 2018, pp. 632-650
- Print publication:
- 01 September 2015
-
- Article
-
- You have access
- Export citation
-
Given a measure
${{\bar{\mu }}_{\infty }}$ on a locally symmetric space 
$Y=\Gamma \backslash G/K$ obtained as a weak-
$*$ limit of probability measures associated with eigenfunctions of the ring of invariant differential operators, we construct a measure ${{\bar{\mu }}_{\infty }}$ on the homogeneous space 
$X=\Gamma \backslash G$ that lifts ${{\bar{\mu }}_{\infty }}$ and is invariant by a connected subgroup 
${{A}_{1}}\subset A$ of positive dimension, where 
$G=NAK$ is an Iwasawa decomposition. If the functions are, in addition, eigenfunctions of the Hecke operators, then ${{\bar{\mu }}_{\infty }}$ is also the limit of measures associated with Hecke eigenfunctions on 
$X$. This generalizes results of the author with A. Venkatesh in the case where the spectral parameters stay away from the walls of the Weyl chamber.
