Notes on the Self-Reducibility of the Weil Representation and Higher-Dimensional Quantum Chaos

2007/08/06 by Shamgar Gurevich, Ronny Hadani, Gurevich, Shamgar +1
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Dynamics and Pattern Formation #Quantum Mechanics and Applications #Quantum chaos and dynamical systems #Representation Theory (math.RT) #math-ph #math.MP #math.RT

paper · pdf · doi:10.48550/arxiv.0708.0755

Notes from the lectures delivered at AGAQ conference (Istanbul, June 2006)

openalex publication_date 2007/08/06 · arxiv created 2009/04/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 A of the torus T^2N=R^2N/Z^2N.

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