par Schillewaert, Jeroen 
;Thas, Koen
Référence Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 7, 080
Publication Publié, 2011
;Thas, KoenRéférence Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 7, 080
Publication Publié, 2011
Article révisé par les pairs
| Résumé : | For Riemannian manifolds there are several examples which are isospectral but not isometric, see e.g. J. Milnor [Proc. Nat. Acad. Sci. USA 51 (1964), 542]; in the present paper, we investigate pairs of domains in R2 which are isospectral but not congruent. All known such counter examples to M. Kac's famous question can be constructed by a certain tiling method ("transplantability") using special linear operator groups which act 2-transitively on certain associated modules. In this paper we prove that if any operator group acts 2-transitively on the associated module, no new counter examples can occur. In fact, the main result is a corollary of a result on Schreier coset graphs of 2-transitive groups. |
