Heisenberg Realizations, Eigenfunctions and Proof of the Kurlberg-Rudnick Supremum Conjecture
Mathematical Physics
2007-05-23 v2 math.MP
Representation Theory
Quantum Physics
Abstract
In this paper, proof of the {\it Kurlberg-Rudnick supremum conjecture} for the quantum Hannay-Berry model is presented. This conjecture was stated in P. Kurlberg's lectures at Bologna 2001 and Tel-Aviv 2003. The proof is a primer application of a fundamental solution: all the Hecke eigenfunctions of the quantum system are constructed. The main tool in our construction is the categorification of the compatible system of realizations of the Heisenberg representation over a finite field. This enables us to construct certain "perverse sheaves" that stands motivically prior to the Hecke eigenfunctions.
Keywords
Cite
@article{arxiv.math-ph/0511036,
title = {Heisenberg Realizations, Eigenfunctions and Proof of the Kurlberg-Rudnick Supremum Conjecture},
author = {Shamgar Gurevich and Ronny Hadani},
journal= {arXiv preprint arXiv:math-ph/0511036},
year = {2007}
}
Comments
Preliminary version, 31 pages