Classical and Quantum Statistical Mechanics of Permutation Representations

Smith, Jonathan D. H.; Baik, Young Gheel; Johnson, Johnson David L.; Kim, Ann Chi

doi:10.1515/9783110807493-024

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Quasigroup Characters1

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2003

2004

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“…In fact, the most natural normalization is obtained by considering the s × s-matrix U whose i, j -entry is [20, (4.7)]. This unitary matrix, known as the unitary character table of P , has an interpretation in terms of quantum mechanics [20]. …”

Section: Quasigroup Charactersmentioning

confidence: 99%

Characters of central piques

Smith

2004

Journal of Algebra

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As a first step towards a duality theory for central quasigroups, the paper presents an explicit computation of the characters of a central pique (quasigroup with pointed idempotent) using Wigner's "little groups" method. The characters of a central pique's cloop (principally isotopic abelian group) form a dual pique. The conjugacy classes of the dual correspond to the characters of the primal; indeed the unitary character table of the dual is the inverse of the unitary character table of the primal. Together with its dual, a central pique forms a structure known as the double. The double satisfies identities indexed by loops of 2-power order. These identities project onto the unit circle to yield identities involving character values.

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Section: Quasigroup Charactersmentioning

confidence: 99%