Representations of affine Lie algebras, parabolic differential equations, and Lamé functions



Duke Mathematical Journal
previous :: next

Representations of affine Lie algebras, parabolic differential equations, and Lamé functions

Pavel I. Etingof and Alexander A. Kirillov, Jr.

Source: Duke Math. J. Volume 74, Number 3 (1994), 585-614.

First Page PDF: View first page of article (PDF, 85 KB)

Primary Subjects: 81R10
Secondary Subjects: 17B67, 33E10, 35Q99, 81T40

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
Alternatively, the document is available for a cost of $25. Select the "buy article" button below to purchase this document from a secured VeriSign, Inc. site.
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077288417
Mathematical Reviews number (MathSciNet): MR1277946
Zentralblatt MATH identifier: 0811.17026
Digital Object Identifier: doi:10.1215/S0012-7094-94-07421-8

References

[ATY] H. Awata, A. Tsuchiya, and Y. Yamada, Integral formulas for the WZNW correlation functions, Nuclear Phys. B 365 (1991), no. 3, 680–696.
Mathematical Reviews (MathSciNet): MR93h:81105
Digital Object Identifier: doi:10.1016/0550-3213(91)90515-Y
[Ber] D. Bernard, On the Wess-Zumino-Witten models on the torus, Nuclear Phys. B 303 (1988), no. 1, 77–93.
Mathematical Reviews (MathSciNet): MR89k:81130
Digital Object Identifier: doi:10.1016/0550-3213(88)90217-9
[BF] D. Bernard and G. Felder, Fock representations and BRST cohomology in ${\rm SL}(2)$ current algebra, Comm. Math. Phys. 127 (1990), no. 1, 145–168.
Mathematical Reviews (MathSciNet): MR91g:17022
Zentralblatt MATH: 0703.17013
Digital Object Identifier: doi:10.1007/BF02096498
[Ch] I. Cherednik, Integral solutions of trigonometric Knizhnik-Zamolodchikov equations and Kac-Moody algebras, Publ. Res. Inst. Math. Sci. 27 (1991), no. 5, 727–744.
Mathematical Reviews (MathSciNet): MR93h:17058
Zentralblatt MATH: 0753.17036
[C] E. T. Copson, Asymptotic expansions, Cambridge Tracts in Mathematics and Mathematical Physics, No. 55, Cambridge University Press, New York, 1965.
Mathematical Reviews (MathSciNet): MR29:6234
Zentralblatt MATH: 0123.26001
[CFW] M. Crivelli, G. Felder, and C. Wieczerkowski, Generalized hypergeometric functions on the torus and adjoint representation of $U_{q}(\mathfrak{sl}_{2})$, preprint.
[E] P. I. Etingof, Representations of affine Lie algebras, elliptic $r$-matrix systems, and special functions, to appear in Comm. Math. Phys. (hep-th 9303018).
Mathematical Reviews (MathSciNet): MR1259404
Digital Object Identifier: doi:10.1007/BF02099981
[FF] B. L. Feigin and E. V. Frenkel, Affine Kac-Moody algebras and semi-infinite flag manifolds, Comm. Math. Phys. 128 (1990), no. 1, 161–189.
Mathematical Reviews (MathSciNet): MR92f:17026
Zentralblatt MATH: 0722.17019
Digital Object Identifier: doi:10.1007/BF02097051
[FR] I. B. Frenkel and N. Yu. Reshetikhin, Quantum affine algebras and holonomic difference equations, Comm. Math. Phys. 146 (1992), no. 1, 1–60.
Mathematical Reviews (MathSciNet): MR94c:17024
Zentralblatt MATH: 0760.17006
Digital Object Identifier: doi:10.1007/BF02099206
[Kri] I. M. Krichever, Methods of algebraic geometry in the theory of nonlinear equations, Russian Math. Surveys 32 (1977), 185–213.
Zentralblatt MATH: 0386.35002
Digital Object Identifier: doi:10.1070/RM1977v032n06ABEH003862
[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.
Mathematical Reviews (MathSciNet): MR87h:81129
Zentralblatt MATH: 0661.17020
Digital Object Identifier: doi:10.1016/0550-3213(84)90374-2
[OP] M. A. Olshanetsky and A. M. Perelomov, Quantum integrable systems related to Lie algebras, Phys. Rep. 94 (1983), no. 6, 313–404.
Mathematical Reviews (MathSciNet): MR84k:81007
Digital Object Identifier: doi:10.1016/0370-1573(83)90018-2
[PS] A. Pressley and G. Segal, Loop groups, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1986.
Mathematical Reviews (MathSciNet): MR88i:22049
Zentralblatt MATH: 0618.22011
[RV] N. Yu. Reshetikhin and A. N. Varchenko, <i/> in preparation.
[SV] V. V. Schechtman and A. N. Varchenko, Arrangements of hyperplanes and Lie algebra homology, Invent. Math. 106 (1991), no. 1, 139–194.
Mathematical Reviews (MathSciNet): MR93b:17067
Zentralblatt MATH: 0754.17024
Digital Object Identifier: doi:10.1007/BF01243909
[TK] A. Tsuchiya and Y. Kanie, Vertex operators in conformal field theory on ${\bf P}\sp 1$ and monodromy representations of braid group, Conformal field theory and solvable lattice models (Kyoto, 1986) eds. M. Jimbo, T. Miwa, and A. Tsuchiya, Adv. Stud. Pure Math., vol. 16, Academic Press, Boston, MA, 1988, pp. 297–372.
Mathematical Reviews (MathSciNet): MR89m:81166
Zentralblatt MATH: 0661.17021
[V] A. N. Varchenko, Critical points of the product of powers of linear functions and families of bases of singular vectors, preprint, 1993.
[WW] E. T. Whittaker and G. N. Watson, Course of Modern Analysis, fourth edition, Cambridge Univ. Press, Cambridge, 1958.
previous :: next

2008 © Duke University Press