Complete set of unitary irreps of Discrete Heisenberg Group $HW_{2^s}$

• URL: http://arxiv.org/abs/2210.04263v2
• Date: Mon, 24 Jun 2024 12:28:47 GMT
• Title: Complete set of unitary irreps of Discrete Heisenberg Group $HW_{2^s}$
• Authors: E. Floratos, I. Tsohantjis,
• Abstract summary: explicit construction of unitary irreducible representations of the discrete finite Heisenberg-Weyl group $HW_2s$ over the discrete phase space lattice. We discuss possible physical applications for finite quantum mechanics and quantum computation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $HW_{2^s}$ 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.

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