Heisenberg Realizations, Eigenfunctions and Proof of the Kurlberg-Rudnick Supremum Conjecture

Details Heisenberg Realizations, Eigenfunctions and Proof of the Kurlberg-Rudnick Supremum Conjecture Heisenberg Realizations, Eigenfunctions and Proof of the Kurlberg-Rudnick Supremum Conjecture

2005-11-10

arxiv.org/abs/math-ph/0511036v2

Physics

Mathematical Physics

Preliminary version, 31 pages

Scientific paper

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.

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