Representations and Properties of Generalized $A_r$ Statistics

Mohammed Daoud

Published 2006-06-20Version 1

A generalization of $A_r$ statistics is proposed and developed. The generalized $A_r$ quantum statistics is completely specified by a set of Jacobson generators satisfying a set of triple algebraic relations. Fock-Hilbert representations and Bargmann-Fock realizations are derived.