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Letters in Mathematical Physics

, Volume 31, Issue 4, pp 315–325 | Cite as

Fusion algebra at a rational level and cohomology of nilpotent subalgebras of\(\widehat{\mathfrak{s}\mathfrak{l}}\)(2)

  • Boris Feigin
  • Feodor Malikov
Article

Abstract

We define and calculate the fusion algebra of a WZW model at a rational level using cohomological methods. As a byproduct, we obtain a cohomological characterization of admissible representations of\(\widehat{\mathfrak{s}\mathfrak{l}}\)2.

Mathematics Subject Classifications (1991)

17B56 17B67 17B81 81T40 

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References

  1. 1.
    Awata, H. and Yamada, Y., Fusion rules for the fractional level\(\widehat{\mathfrak{s}\mathfrak{l}}\)(2) algebra, KEK-TH-316 KEK Preprint 91-209, January 1992.Google Scholar
  2. 2.
    Bauer, M. and Sochen, N., Singular vectors by fusions inA 1(1), Saclay preprint SPht/91-117 (1991).Google Scholar
  3. 3.
    Feigin, B. and Fuchs, D.,J. Geom. Phys. 5, 209–235 (1988).Google Scholar
  4. 4.
    Feigin, B. and Frenkel, E.,Phys. Lett. B 246, 75 (1990).Google Scholar
  5. 5.
    Fuchs, D. B.Funktsional Anal. i Prilozhen 23(2), 81–83 (1989).Google Scholar
  6. 6.
    Furlan, P., Ganchev, A. Ch., Paunov, R., and Petkova, V. B.,Phys. Lett. 267 63 (1991); Solutions of the Knizhnik-Zamolodchikov equations with rational isospins and the reduction to the minimal models, preprint CERN-TH.6289/91, accepted for publication inNuclear Phys. B. Google Scholar
  7. 7.
    Kac, V. G. and Wakimoto, M.,Proc. Nat'l Acad. Sci. USA (1988) 4956.Google Scholar
  8. 8.
    Kazhdan, D. and Lusztig, G.,Duke Math. J. 62, 21-29.Google Scholar
  9. 9.
    Malikov, F. G., Feigin, B. L., and Fuchs, D. B.,Funktsional. Anal. i Prilozhen 20(2), (1988) 25–37.Google Scholar
  10. 10.
    Malikov, F.,Infinite Analysis - Proc. RIMS Research Project 1991, Part B, 623-645, World Scientific, Singapore.Google Scholar
  11. 11.
    Malikov F.,Leningrad Math. J. 2 (1991) 269–286.Google Scholar
  12. 12.
    Mathieu, P. and Walton, M.,Prog. Theor. Phys. Suppl. 102, 229 (1990).Google Scholar
  13. 13.
    Segal, G., inProc. XI Internat. Congress on Math. Phys., 17-27 July 1988, Swansea, Adam Hilger, Bristol, New York, 1988.Google Scholar
  14. 14.
    Tsuchiya, A., Ueno, K., and Yamada Y.,Adv. Stud. Pure Math. 19, Academic Press, Boston, 1989, 459–566.Google Scholar
  15. 15.
    Verlinde, E.,Nuclear Phys. B 300, 360 (1988).Google Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Boris Feigin
    • 1
  • Feodor Malikov
    • 2
  1. 1.Landau Institute for Theoretical PhysicsMoscowRussia
  2. 2.Department of MathematicsYale UniversityNew HavenUSA

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