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<p>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 <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_5888_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="45" /> </InlineMediaObject> <EquationSource Format="TEX">\(HW_{2^{s}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>H</mi> <msub> <mi>W</mi> <msup> <mn>2</mn> <mi>s</mi> </msup> </msub> </mrow> </math></EquationSource> </InlineEquation> over the discrete phase space lattice <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_5888_Article_IEq4.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {Z}_{2^{s}}\otimes \)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="double-struck">Z</mi> <msup> <mn>2</mn> <mi>s</mi> </msup> </msub> <mo>⊗</mo> </mrow> </math></EquationSource> </InlineEquation> <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10773_2025_5888_Article_IEq5.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb {Z}_{2^{s}}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="double-struck">Z</mi> <msup> <mn>2</mn> <mi>s</mi> </msup> </msub> </math></EquationSource> </InlineEquation> is presented. We explicitly determine their characters and their fusion rules. We discuss possible physical applications for finite quantum mechanics and quantum computation.</p>

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Complete Set of Unitary Irreps of Discrete Heisenberg Group \( HW_{2^{s}}\)

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  • 发表日期：

    2025年1月18日

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  • E. Floratos,
  • I. Tsohantjis

摘要

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 \(HW_{2^{s}}\) H W 2 s over the discrete phase space lattice \(\mathbb {Z}_{2^{s}}\otimes \) Z 2 s ⊗ \(\mathbb {Z}_{2^{s}}\) 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.