We review an elementary approach to the construction of all irreducible representations of the finite Heisenberg group. Determining the number of inequivalent classes of irreducible representations by different methods leads to an identity of sums involving greatest common divisors. We show how this identity can be generalized and derive an explicit formula for the sums.
Daniel Bump;Persi Diaconis;Angela Hicks;Laurent Miclo;Harold Widom, 2017, An Exercise(?) in Fourier Analysis on the Heisenberg Group, Annales de la faculté des sciences de Toulouse Mathématiques, 26, 2, pp. 263-288, 10.5802/afst.1533, https://doi.org/10.5802/afst.1533.