2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72508In its most general formulation a quantum kinematical system is described by a Heisenberg group; the "configuration space" in this case corresponds to a maximal isotropic subgroup. We study irreducible models for Heisenberg groups based on compact maximal isotropic subgroups. It is shown that if the Heisenberg group is 2-regular, but the subgroup is not, the "vacuum sector" of the irreducible representation exhibits a fermionic structure. This will be the case, for instance, in a quantum mechanical model based on the 2-adic numbers with a suitably chosen isotropic subgroup. The formulation in terms of Heisenberg groups allows a uniform treatment of p-adic quantum systems for all primes p, and includes the possibility of treating adelic systems.14 pages, 1 figure. To be published in "Infinite Dimensional Analysis, Quantum Probability and Related Topics" (IDAQP). Added 2 referencesQuantum AlgebraMathematical Physics81R99 (Primary) 20K10, 20K35 (Secondary)text