ON THE ALGEBRAIC STRUCTURE OF DYSON’S CIRCULAR ENSEMBLES

抄録

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.