Representations and Properties of Generalized $A_r$ Statistics

Abstract

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.

12 pages, to appear in IJMPA (2006)

References in corpus (6)

• Quantum Hall Effect in Higher Dimensions
• Coherent States for the Hydrogen Atom
• Black Hole Statistics
• The effective action for edge states in higher dimensional quantum Hall systems
• Quantum Hall Effect on Higher Dimensional Spaces
• Fractional supersymmetric Quantum Mechanics as a set of replicas of ordinary supersymmetric Quantum Mechanics

Cited by in corpus (1)

• Chiral bosons on Bargmann space associated with A${}_r$ Statistics