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On algebraic equations satisfied by hypergeometric correlators in WZW models. II

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The paper contains an explicit description of genus 0 conformal block bundles for Wess-Zumino-Witten models of Conformal field theory. We prove that an earlier construction due to the second and the third authors gives a map of these bundles to certain de Rham cohomology bundles.

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References

  • [B] Bourbaki, N.: Groupes et Algèbres de Lie. Chap. VII, VIII, Paris: Hermann, 1975

    Google Scholar 

  • [FSVA] Feigin, B., Schechtman, V., Varchenko, A.: On algebraic equations satisfied by correlators in Wess-Zumino-Witten models. Lett. Math. Phys.20, 291–297 (1990)

    Article  Google Scholar 

  • [FSV1] Feigin, B., Schechtman, V., Varchenko, A.: On algebraic equations satisfied by hypergeometric correlators in WZW models. I. Commun. Math. Phys.163, 173–184 (1994)

    Google Scholar 

  • [F] Finkelberg, M.: An equivalence of fusion categories. Ph.D. Thesis, Harvard (1993), submitted to press

  • [K] Kac, V.: Infinite dimensional Lie algebras. Cambridge: Cambridge Univ. Press, 1985

    Google Scholar 

  • [KL] Kazhdan, D., Lusztig, G.: Tensor categories arising from affine Lie algebras. I–IV. J. Am. Math. Soc.6, 905–947 (1993); ibid., 949–1011;7, 335–382 (1994); ibid., 383–454

    Google Scholar 

  • [KZ] Knizhnik, A., Zamolodchikov, A.: Current algebra and Wess-Zumino model in two dimensions. Nucl. Phys.B247, 83–103 (1984)

    Article  Google Scholar 

  • [SVB] Schechtman, V., Varchenko, A.: Integral representations of N-point conformal correlators in the WZW model. Preprint MPI/89-51, Max Planck Institut, Bonn (1989), 1–21

    Google Scholar 

  • [SV] Schechtman, V., Varchenko, A.: Arrangements of hyperplanes and Lie algebra homology. Inv. Math.100, 134–194, (1991)

    Google Scholar 

  • [TK] Tsuchya, A., Kanie, V.: Vertex operators in conformal field theory on ℙ1 and monodromy representations of braid groups. Adv. Stud. Pure Math.16, 297–372, (1988)

    Google Scholar 

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Communicated by G. Felder

The second author was supported in part by the NSF grant DMS-9202280. The third author was supported in part by the NSF grant DMS-9203939.

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Feigin, B., Schechtman, V. & Varchenko, A. On algebraic equations satisfied by hypergeometric correlators in WZW models. II. Commun.Math. Phys. 170, 219–247 (1995). https://doi.org/10.1007/BF02099447

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  • DOI: https://doi.org/10.1007/BF02099447

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