Complete set of unitary irreps of Discrete Heisenberg Group $H{W}_{2^s}$

Abstract

Following the method of induced group representations of Wigner-Mackay, the explicit construction of all the unitary irreducible representations of the discrete finite Heisenberg-Weyl group $H{W}_{2^s}$ over the discrete phase space lattice $Z_{2^s}$ $\otimes$ $Z_{2^s}$ is presented. We explicitly determine their characters and their fusion rules. We discuss possible physical applications for finite quantum mechanics and quantum computation.

25 pages

References in corpus (1)

• The Hilbert Space of Quantum Gravity Is Locally Finite-Dimensional

Cited by in corpus (1)

• Construction of Metaplectic Representations of $S{L}_2({\mathbb{Z}}_{2^n})$ and Twisted Magnetic Translations