Harmonic Analysis on the Finite Twisted Poincaré Upper Half Plane
Jorge Vargas and Jorge Soto-Andrade
We prove that the induced representation from a non trivial character of the Coxeter torus of GL$(2,F)$, for a finite field $F$, is multiplicity-free; we give an explicit description of the corresponding (twisted) spherical functions and a version of the Heisenberg Uncertainty Principle.