The Unitary Dual of the Heisenberg Group Over \(\mathfrak {R}_p\)

In this short note, we review the essentials of the representation theory of the Heisenberg group over a certain compact ring obtained as the direct product of infinite copies of the finite field \(\mathbb {F}_p\) , where p is a prime number, and we use it to calculate the spectrum of the Vladimirov-Taibleson operator on the group.