Tannaka-Krein duality for compact matrix pseudogroups. TwistedSU(N) groups
The notion of concrete monoidalW*-category is introduced and investigated. A generalization of the Tannaka-Krein duality theorem is proved. It leads to new examples of compact matrix pseudogroups. Among them we have twistedSU(N) groups denoted bySμU(N). It is shown that the representation theory forSμU(N) is similar to that ofSU(N): irreducible representations are labeled by Young diagrams and formulae for dimensions and multiplicity are the same as in the classical case.
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- 1.Bucur, I., Deleanu, A.: Introduction to the theory of categories and functors. A. Wiley, Interscience Publications. London-New York-Sydney: John Wiley and Sons LTD, 1968Google Scholar
- 2.Drinfeld, V.G.: Quantum groups. Proceedings ICM (1986)Google Scholar
- 3.Ghez, P., Lima, R., Roberts, J.E.:W *-categories. Preprint CPT CNRS Marseille; see also Ghez, P.: A survey ofW *-categories, Operator algebra and applications, Part 2 (Kingston Ont. 1980). Symp. Pure Math.38, 137 (1982)Google Scholar
- 4.Goodman, F.M., Harpe, P., de la, Jones, V.F.R.: Coxeter-Dynkin diagrams and towers of algebras, chapter 2. Preprint IHES/M. 87/6Google Scholar
- 5.Wenzl, H.: Representations of Hecke algebras and subfactors. Thesis Univ. of Pennsylvania 1985Google Scholar
- 6.Woronowicz, S.L.: Duality in theC *-algebra theory. Proceedings ICM, p. 1347 (part II) (1982)Google Scholar
- 7.Woronowicz, S.L.: TwistedSU(2) group. An example of a non-commutative differential calculus, R.I.M.S. Publ. Kyoto University,23, (No 1) 117–181 (1987)Google Scholar
- 8.Woronowicz, S.L.: Compact matrix pseudogroups. Commun. Math. Phys.111, 613–665 (1987)Google Scholar