Skip to main content
SpringerLink
Log in

Coherent state operators and n-point invariants for U q ((sl(2))

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

Abstract

We write down a complete set of n-point Uq(sl(2)) invariants (using a polynomial basis for the irreducible finite dimensional U q -modules) that are regular for all nonzero values of the deformation parameter q.

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. FaddeevL. D., ReshetikhinN. Yu., and TakhtajanL. A., Algebra and Analysis 1(1), 178 (1989). (English transl.: Leningrad Math. J. 1, 193 (1990)) and earlier references cited there.

    Google Scholar 

  2. DrinfeldV. G., Quantum groups, Proc. 1986 ICM, col. 1 (Amer. Math. Soc., Berkeley, CA 1987) 798; Algebra and Analysis 1(2), 178 (1989) (English transl.: Leningrad Math. J. 1, 321 (1990)).

    Google Scholar 

  3. JimboM., Lett. Math. Phys. 10, 63 (1985); 11, 247 (1986).

    Google Scholar 

  4. WoronowiczS. L., Twisted SU(2) group, an example of a non-commutative differential geometry, Publ. RIMS Kyoto 23, 117 (1987); Comm. Math. Phys. 122, 125 (1989).

    Google Scholar 

  5. KirillovA. N. and ReshetikhinN. Yu., Representations of the algebra 319-1, q-orthogonal polynomials and invariants of links, in V.Kac (ed), Infinite Dimensional Lie Algebras and Groups, Proc. 1988 CIRM Luminy Conference, World Scientific, Singapore, 1989, p. 285.

    Google Scholar 

  6. GanchevA. Ch. and PetkovaV. B., Phys. Lett. B233, 374 (1989).

    Article  Google Scholar 

  7. RueggH., J. Math. Phys. 31, 1085 (1990).

    Article  Google Scholar 

  8. TodorovI. T., Quantum groups as symmetries of chiral conformal algebras, Lectures at the 1989 Clausthal-Zellerfeld Workshop on Mathematical Physics, Lecture Notes in Physics, 370, 231, Springer, Berlin, 1990.

    Google Scholar 

  9. PerelomovA. M., Comm. Math. Phys. 26, 222 (1972); Generalized Coherent States and their Applications, Springer, New York, 1986.

    Google Scholar 

  10. HadjiivanovL. K., PaunovR. R., and TodorovI. T., Nuclear Phys. (Methods in Theor. Phys.) B 356, 387 (1991); Nuclear Phys. (Proc. Suppl.) 18B, 141 (1990).

    Google Scholar 

  11. VaksmanL. L. and Soibel'manYa. S., Funktsional Anal.i Prilozhen 22(3), 1 (1988) (transl.: Functional Anal. Appl. 22 170 (1988).

    Google Scholar 

  12. LusztigG., Adv. in Math. 70, 237 (1988); J. Amer. Math. Soc. 3, 257, 447 (1990).

    Google Scholar 

  13. RossoM., Comm. Math. Phys. 117, 581 (1988).

    Google Scholar 

  14. PasquierV. and SaleurH., Nuclear Phys. B330, 523 (1990).

    Article  Google Scholar 

  15. Fröhlich, J. and Kerler, T., On the role of quantum groups in low dimensional local quantum field theories, ETH Zürich preprint (1990).

  16. De Concini, G. and Kac, V. G., Representations of quantum groups at roots of 1, Scuola Normale Superiore, Pisa preprint 75 (1990).

  17. Gel'fandI. M. and ZelevinskiA. V., Funktsional Anal. i Prilozhen 18(3), 14 (1984), (transl.: Functional Anal. Appl. 18, 183 (1984).

    Google Scholar 

  18. Biedenharn, L. C. and Lohe, M. A., Induced representations and tensor operators for quantum groups, Duke Univ. preprint 1991.

  19. Alvarez-GauméL., GómezC., and SierraG., Nuclear Phys. B330, 347 (1990).

    Article  Google Scholar 

  20. Baulieu, L. and Floratos, E. G., Path integral on the quantum plane, Paris preprint LPTENS 90-34, PAR-LPTHE 90-54.

  21. Hadjiivanov, L. K., Paunov, R. R., Todorov, I. T., U q -covariant oscillators and vertex operators, Trieste-Paris preprint, SISSA/ISAS 1/91/FM, IPNO/TH 91/25.

  22. Gawedzki, K., Classical origin of quantum group symmetries in Wess-Zumino-Witten conformal field theory, Bures-sur-Yvette preprint IHES/P/90/92.

Download references

Author information

Author notes

  1. Yassen S. Stanev

    Present address: Institute for Nuclear Research and Nuclear Energy, BG-1784, Sofia, Bulgaria

  2. Ivan T. Todorov

    Present address: Unité de Recherche des Universités Paris XI, Paris, France

Authors and Affiliations

  1. Dipartimento di Fisica Teorica dell' Università di Trieste, Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste, Italy

    Paolo Furlan

  2. International School for Advanced Studies (SISSA/ISAS), Trieste, Italy

    Yassen S. Stanev

  3. Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Trieste, Italy

    Yassen S. Stanev

  4. Insitut des Hautes Etudes Scientifiques, F-91440, Bures-sur-Yvette, France

    Ivan T. Todorov

  5. Division de Physique Théorique, Institut de Physique Nucléaire, F-91406, Orsay Cedex, France

    Ivan T. Todorov

Authors
  1. Paolo Furlan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yassen S. Stanev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ivan T. Todorov
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Furlan, P., Stanev, Y.S. & Todorov, I.T. Coherent state operators and n-point invariants for U q ((sl(2)). Lett Math Phys 22, 307–319 (1991). https://doi.org/10.1007/BF00405606

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00405606

AMS subject classifications (1991)

Search

Navigation