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Complete set of unitary irreps of Discrete Heisenberg Group $HW_{2^s}$ (2210.04263v3)

Published 9 Oct 2022 in quant-ph, hep-th, math-ph, and math.MP

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 $HW_{2s}$ over the discrete phase space lattice $Z_{2s}$ $\otimes$ $Z_{2s}$ is presented. We explicitly determine their characters and their fusion rules. We discuss possible physical applications for finite quantum mechanics and quantum computation.

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