Skip to main content
Log in

On the Haar measure of the quantumSU(N) group

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

We prove that the Haar state associated to the compact matrix quantum groupSU μ(N) is faithful for μ∈]−1,1[,μ≠0, and anyN≧2.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • [Br] Bragiel, K.: The twistedSN(N). On theC *-algebraC(SU μ(N)). Lett. Math. Phys.20, 251–257 (1990)

    Article  Google Scholar 

  • [BS] Baaj, S., Skandalis, G.: Unitaires multiplicatifs et dualite pur les produits croisses deC *-algebres. Preprint 1990

  • [Dr] Drinfeld, V.: Quantum Groups, I.C.M. Berkeley 1986

  • [Ji] Jimbo, M.: Aq-analogue of\(U(\mathfrak{g}\mathfrak{l}(N + 1))\), Hecke algebras and Yang-Baxter equation. Lett. Math. Phys.11, 247–252 (1986)

    Article  Google Scholar 

  • [KL] Klimek, S., Lesniewski, A.: Quantum Riemann surfaces I. Preprint 1991

  • [La] Lance, E.C.: On nuclearC *-algebras. J. Funct. Anal.12, 157–176 (1973)

    Article  Google Scholar 

  • [Na] Nagy, G.: Thesis, Berkeley (in preparation)

  • [Ro] Rosso, M.: Algebres envelopantes quantifiees, groupes quantiques compacts de matrices et calcul differentiel non-commutativ. Duke Math. J.61, No. 1, 11–40 (1990)

    Article  Google Scholar 

  • [Sh1] Sheu, A.J.-L.: Quantization of the PoissonSU(2) and its Poisson homogeneous space—the sphere (with an Appendix by Lu, J.-H., Weinstein, A.). Commun. Math. Phys.135, 217–232 (1990)

    Google Scholar 

  • [Sh2] Sheu, A.J.-L.: The Weyl quantization of PoissonSU(2). Preprint 1992

  • [So1] Soibelman, Ya.S: Irreducible representations of the function algebra on the quantum groupSU(n), and Schubert cells. Soviet Math. Dokl.40, No. 1, 34–38 (1990)

    Google Scholar 

  • [So2] Soibelman, Ya.S.: The algebra of functions on a compact quantum group, and its representations. Leningrad Math. J.2, No. 1, 161–178 (1990)

    Google Scholar 

  • [St] Strătilă, Ş.: Modular theory for operator algebras. Abacus 1981

  • [VS1] Vaksman, L.L., Soibelman, Ya.S.: Algebra of functions of quantumSU(2). Funkt. Anal. i ego Priloz.22, 1–14 (1988) (in Russian)

    Google Scholar 

  • [VS2] Vaksman, L.L., Soibelman, Ya.S.: Algebra of functions on quantumSU(n+1) group and odd dimensional quantum spheres. Algebra i Analiz2, No. 5, 101–120 (1990) (in Russian)

    Google Scholar 

  • [Wo1] Woronowicz, S.L.: TwistedSU(2) group. An example of non-commutative differential calculus. Publ. R.I.M.S.23, 117–181 (1987)

    Google Scholar 

  • [Wo2] Woronowicz, S.L.: Compact matrix pseudogroups. Commun. Math. Phys.111, 613–665 (1987)

    Article  Google Scholar 

  • [Wo3] Woronowicz, S.L.: Tannaka-Krein duality for compact matrix pseudogroups. TwistedSU(N) group. Invent. Math.93, 35–76 (1988)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by N.Yu. Reshetikhin

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nagy, G. On the Haar measure of the quantumSU(N) group. Commun.Math. Phys. 153, 217–228 (1993). https://doi.org/10.1007/BF02096641

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02096641

Keywords

Navigation