Skip to main content
SpringerLink
Log in

Highest weight representations of quantum current algebras

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

Abstract

We study the highest weight and continuous tensor product representations ofq-deformed Lie algebras through the mappings of a manifold into a locally compact group. As an example the highest weight representation of theq-deformed algebra slq(2,ℂ) is calculated in detail.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Albeverio, S., Høegh-Krohn, R., Marion, J., Testard, D., and Torrésani, B.:Noncommutative Distributions, Unitary Representation of Gauge Groups and Algebras, Monographs Textbooks Pure Appl. Math. 175, Marcel Dekker, New York, 1993.

    Google Scholar 

  2. Jimbo, M.:Lett. Math. Phys. 10 (1985), 63;11 (1986), 247;Comm. Math. Phys. 102 (1986) 537.

    Google Scholar 

  3. Frenkel, I. B. and Reshetikhin, N. Y.Comm. Math. Phys. 146 (1992), 1–60.

    Google Scholar 

  4. Delius, G. and Zhang, Y. Z.:J. Phys. A 28 (1995), 1915–1927.

    Google Scholar 

  5. Flato, M. and Lu, Z.:Lett. Math. Phys. 21 (1991), 85; Flato, M. and Sternheimer, D.:Lett. Math. Phys. 22 (1991), 155.

    Google Scholar 

  6. Fei, S. M.:J. Phys. A 24 (1991), 5195–5214; Fei, S. M. and Guo, H. Y.:Comm. Theoret. Phys. 20 (1993), 299–312.

    Google Scholar 

  7. Torrésani, B.: Unitary highest weight representations of gauge groups, in S. Albeverio, J. E. Fenstad, H. Holden, T. Lindstrøm, (eds),Ideas and Methods in Mathematical Analysis, Stochastics, and Applications, Vol. I, Cambridge University Press, 1992, pp. 332–343.

  8. Drinfeld, V. G.:Soviet Math. Dokl. 32 (1985), 254;Proc. I.C.M. Berkeley (1986), 798–820; Faddeev, L. D.:Leningrad Math. J. 1 (1) (1990).

    Google Scholar 

  9. Guichardet, A.:Symmetric Hilbert Space and Related Topics, Lecture Notes in Math. 261, Springer, Berlin, 1972.

    Google Scholar 

  10. Curtright, T. L., Ghandour, G. I., and Zachos, C. K.:J. Math. Phys. 32 (1991), 3; Curtright, T. L. and Zachos, C. K.:Phys. Lett. B 243 (1990), 237.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ruhr-University Bochum, D-44780, Bochum, Germany

    Sergio Albeverio & Shao-Ming Fei

Authors
  1. Sergio Albeverio
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shao-Ming Fei
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Alexander von Humboldt-Stiftung fellow. On leave from Institute of Physics, Chinese Academy of Sciences, Beijing, P.R. China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Albeverio, S., Fei, SM. Highest weight representations of quantum current algebras. Lett Math Phys 36, 319–326 (1996). https://doi.org/10.1007/BF00943284

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00943284

Mathematics Subject Classifications (1991)

Key words

Search

Navigation