ON THE ALGEBRAIC STRUCTURE OF DYSON’S CIRCULAR ENSEMBLES

Jonathan D.H. Smith

doi:10.32219/isms.76.2_289

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Keywords: circular orthogonal ensemble, circular unitary ensemble, circular symplectic ensemble, Haar measureMoufang loop, Moufang loop, right quasigroup, symmetric space, core, twisted subset, twisted subgroup

JOURNAL FREE ACCESS

2013 Volume 76 Issue 2 Pages 289-298

DOI https://doi.org/10.32219/isms.76.2_289

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Abstract

Dyson’s Circular Orthogonal, Unitary, and Symplectic Ensembles are measure spaces modeling families of physical systems with specific spin and timereversal properties. In this paper, it is shown that each of the three ensembles carries a transitive right quasigroup structure, such that automorphisms of the measure space are automorphisms of the quasigroup structure.

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