Notes on the Self-Reducibility of the Weil Representation and Higher-Dimensional Quantum Chaos
Mathematical Physics
2009-04-24 v3 math.MP
Representation Theory
Abstract
In these notes we discuss the "self-reducibility property" of the Weil representation. We explain how to use this property to obtain sharp estimates of certain higher-dimensional exponential sums which originate from the theory of quantum chaos. As a result, we obtain the Hecke quantum unique ergodicity theorem for generic linear symplectomorphism of the torus $T^{2N}=R^{2N}/Z^{2N}.
Keywords
Cite
@article{arxiv.0708.0755,
title = {Notes on the Self-Reducibility of the Weil Representation and Higher-Dimensional Quantum Chaos},
author = {Shamgar Gurevich and Ronny Hadani},
journal= {arXiv preprint arXiv:0708.0755},
year = {2009}
}
Comments
Notes from the lectures delivered at AGAQ conference (Istanbul, June 2006)