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Tannaka-Krein duality for compact matrix pseudogroups. Twisted SU(N) groups. (English) Zbl 0664.58044

The notion of concrete monoidal \(W^*\)-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 twisted SU(N) groups denoted by \(S_{\mu}U(N)\). It is shown that the representation theory for \(S_{\mu}U(N)\) is similar to that of SU(N): irreducible representations are labeled by Young diagrams and formulae for dimensions and multiplicity are the same as in the classical case.

MSC:

58H05 Pseudogroups and differentiable groupoids
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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, 1968 · Zbl 0197.29205
[2] Drinfeld, V.G.: Quantum groups. Proceedings ICM (1986)
[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)
[4] Goodman, F.M., Harpe, P., de la, Jones, V.F.R.: Coxeter-Dynkin diagrams and towers of algebras, chapter 2. Preprint IHES/M. 87/6 · Zbl 0698.46050
[5] Wenzl, H.: Representations of Hecke algebras and subfactors. Thesis Univ. of Pennsylvania 1985
[6] Woronowicz, S.L.: Duality in theC *-algebra theory. Proceedings ICM, p. 1347 (part II) (1982)
[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) · Zbl 0676.46050 · doi:10.2977/prims/1195176848
[8] Woronowicz, S.L.: Compact matrix pseudogroups. Commun. Math. Phys.111, 613-665 (1987) · Zbl 0627.58034 · doi:10.1007/BF01219077
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