Heisenberg Realizations, Eigenfunctions and Proof of the Kurlberg-Rudnick Supremum Conjecture
Gurevich, Shamgar ; Hadani, Ronny
arXiv, 0511036 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2005-11-09
Classification:  Mathematical Physics,  Mathematics - Representation Theory,  Quantum Physics 
@article{0511036,
     author = {Gurevich, Shamgar and Hadani, Ronny},
     title = {Heisenberg Realizations, Eigenfunctions and Proof of the
  Kurlberg-Rudnick Supremum Conjecture},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0511036}
}

Gurevich, Shamgar; Hadani, Ronny. Heisenberg Realizations, Eigenfunctions and Proof of the
  Kurlberg-Rudnick Supremum Conjecture. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0511036/