Irreducible tensor operators in the regular coaction formalisms of compact quantum group algebras

John Francis Cornwell

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

The defining conditions for the irreducible tensor operators associated with the unitary irreducible corepresentations of compact quantum group algebras are deduced first in both the right and left regular coaction formalisms. In each case it is shown that there are two types of irreducible tensor operator, which may be called ''ordinary'' and ''twisted.'' The consistency of the definitions is demonstrated, and various consequences are deduced, including generalizations of the Wigner-Eckart theorem for both the ordinary and twisted operators. Also included are discussions (within the regular coaction formalisms for compact quantum group algebras) of inner-products, basis functions, projection operators, Clebsch-Gordan coefficients, and two types of tensor product of corepresentations. The formulation of quantum homogeneous spaces for compact quantum group algebras is discussed, and the defining conditions for the irreducible tensor operators associated with such quantum homogeneous spaces and with the unitary irreducible corepresentations of the compact quantum group algebras are then deduced. There are two versions, which correspond to restrictions of the right and left regular coactions. In each case it is again shown that there are ordinary and twisted irreducible tensor operators. Various consequences are deduced, including the corresponding generalizations of the Wigner-Eckart theorem. (C) 1996 American Institute of Physics.

Original languageEnglish
Pages (from-to)4590-4634
Number of pages45
JournalJournal of Mathematical Physics
Volume37
Publication statusPublished - Sept 1996

Keywords

  • WIGNER-ECKART THEOREM
  • MATRIX PSEUDOGROUPS
  • DUALITY
  • SUQ(2)

Fingerprint

Dive into the research topics of 'Irreducible tensor operators in the regular coaction formalisms of compact quantum group algebras'. Together they form a unique fingerprint.

Cite this