Duke Mathematical Journal

Quantum Knizhnik-Zamolodchikov equations and holomorphic vector bundles

Pavel I. Etingof

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Source
Duke Math. J., Volume 70, Number 3 (1993), 591-615.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1077290890

Digital Object Identifier
doi:10.1215/S0012-7094-93-07013-5

Mathematical Reviews number (MathSciNet)
MR1224100

Zentralblatt MATH identifier
0796.17012

Subjects
Primary: 39A10: Difference equations, additive
Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 32L10: Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30] 81R50: Quantum groups and related algebraic methods [See also 16T20, 17B37]

Citation

Etingof, Pavel I. Quantum Knizhnik-Zamolodchikov equations and holomorphic vector bundles. Duke Math. J. 70 (1993), no. 3, 591--615. doi:10.1215/S0012-7094-93-07013-5. https://projecteuclid.org/euclid.dmj/1077290890


Export citation

References

  • [Ao] K. Aomoto, A note on holonomic $q$-difference systems, Algebraic analysis, Vol. I eds. M. Kashiwara and T. Kawai, Academic Press, Boston, MA, 1988, pp. 25–28.
  • [A] M. F. Atiyah, Vector bundles over an elliptic curve, Proc. London Math. Soc. (3) 7 (1957), 414–452.
  • [CP] V. Chari and A. Pressley, Quantum affine algebras, Comm. Math. Phys. 142 (1991), no. 2, 261–283.
  • [Ch] I. V. Cherednik, Quantum Knizhnik-Zamolodchikov equations and affine root systems, preprint, 1992.
  • [D] V. G. Drinfeld, Hopf algebras and the quantum Yang-Baxter equation, Soviet Math. Dokl. 32 (1985), 254–258.
  • [FR] I. B. Frenkel and N. Yu. Reshetikhin, Quantum affine algebras and holonomic difference equations, Comm. Math. Phys. 146 (1992), no. 1, 1–60.
  • [J1] M. Jimbo, A $q$-difference analogue of $U(\germ g)$ and the Yang-Baxter equation, Lett. Math. Phys. 10 (1985), no. 1, 63–69.
  • [J2] M. Jimbo, A $q$-analogue of $U(\germ g\germ l(N+1))$, Hecke algebra, and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), no. 3, 247–252.
  • [K] M. Karoubi, $K$-theory, Grundlehren der Mathematischen Wissenschaften, vol. 226, Springer-Verlag, Berlin, 1978.
  • [Ka] M. Kashiwara, Crystalizing the $q$-analogue of universal enveloping algebras, Comm. Math. Phys. 133 (1990), no. 2, 249–260.
  • [KZ] V. G. Knizhnik and A. B. Zamolodchikov, Current algebra and Wess-Zumino model in two dimensions, Nuclear Phys. B 247 (1984), no. 1, 83–103.
  • [M] A. Matsuo, Jackson integrals of Jordan-Pochhammer type and quantum Knizhnik-Zamolodchikov equation, to appear in Comm. Math. Phys.
  • [Mi] J. W. Milnor and J. D. Stasheff, Characteristic classes, Princeton University Press, Princeton, N. J., 1974.
  • [Mu] D. Mumford, Projective invariants of projective structures and applications, Proc. Internat. Congr. Mathematicians (Stockholm, 1962), Inst. Mittag-Leffler, Djursholm, 1963, pp. 526–530.
  • [NS] M. S. Narasimhan and C. S. Seshadri, Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math. (2) 82 (1965), 540–567.
  • [R] N. Yu. Reshetikhin, Jackson-type integrals, Bethe vectors, and solutions to a difference analog of the Knizhnik-Zamolodchikov system, preprint, 1992.
  • [SV] V. V. Schechtman and A. N. Varchenko, Arrangements of hyperplanes and Lie algebra homology, Invent. Math. 106 (1991), no. 1, 139–194.