Duke Mathematical Journal

A solution to quantum Knizhnik-Zamolodchikov equations and its application to eigenvalue problems of the Macdonald type

Katsuhisa Mimachi
Source: Duke Math. J. Volume 85, Number 3 (1996), 635-658.
First Page: Show Hide
Primary Subjects: 17B81
Secondary Subjects: 05E05, 33D80
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
Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077243445
Mathematical Reviews number (MathSciNet): MR1422360
Zentralblatt MATH identifier: 0889.17009
Digital Object Identifier: doi:10.1215/S0012-7094-96-08524-5

References

[1] K. Aomoto and Y. Kato, Connection formula of symmetric $A$-type Jackson integrals, Duke Math. J. 74 (1994), no. 1, 129–143.
Mathematical Reviews (MathSciNet): MR95b:33052
Zentralblatt MATH: 0802.33016
Digital Object Identifier: doi:10.1215/S0012-7094-94-07406-1
Project Euclid: euclid.dmj/1077288012
[2] H. Awata, S. Odake, and J. Shiraishi, Integral representations of the Macdonald symmetric functions, preprint (q-alg/9506006).
[3] I. Cherednik, Quantum Knizhnik-Zamolodchikov equations and affine root systems, Comm. Math. Phys. 150 (1992), no. 1, 109–136.
Mathematical Reviews (MathSciNet): MR94a:17019
Zentralblatt MATH: 0849.17025
Digital Object Identifier: doi:10.1007/BF02096568
Project Euclid: euclid.cmp/1104251785
[4] I. Cherednik, Double affine Hecke algebras, Knizhnik-Zamolodchikov equations, and Macdonald's operators, Internat. Math. Res. Notices (1992), no. 9, 171–180.
Mathematical Reviews (MathSciNet): MR94b:17040
Zentralblatt MATH: 0770.17004
Digital Object Identifier: doi:10.1155/S1073792892000199
[5] I. Cherednik, Induced representations of double affine Hecke algebras and applications, Math. Res. Lett. 1 (1994), no. 3, 319–337.
Mathematical Reviews (MathSciNet): MR96i:17022
Zentralblatt MATH: 0837.20052
[6] I. Cherednik, Difference-elliptic operators and root systems, Internat. Math. Res. Notices (1995), no. 1, 43–58 (electronic).
Mathematical Reviews (MathSciNet): MR96k:58106
Zentralblatt MATH: 0824.17029
Digital Object Identifier: doi:10.1155/S1073792895000043
[7] 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
Project Euclid: euclid.cmp/1104249974
[8] 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.
Mathematical Reviews (MathSciNet): MR87k:17011
Zentralblatt MATH: 0602.17005
Digital Object Identifier: doi:10.1007/BF00400222
[9] S. Kato, $R$-matrix arising from affine Hecke algebras and its application to Macdonald's difference operators, Comm. Math. Phys. 165 (1994), no. 3, 533–553.
Mathematical Reviews (MathSciNet): MR96h:20028
Zentralblatt MATH: 0820.17023
Digital Object Identifier: doi:10.1007/BF02099422
Project Euclid: euclid.cmp/1104271412
[10] T. H. Koornwinder, Askey-Wilson polynomials for root systems of type $BC$, Hypergeometric functions on domains of positivity, Jack polynomials, and applications (Tampa, FL, 1991) ed. D. St. P. Richards, Contemp. Math., vol. 138, Amer. Math. Soc., Providence, RI, 1992, pp. 189–204.
Mathematical Reviews (MathSciNet): MR94e:33039
Zentralblatt MATH: 0797.33014
[11] G. Lusztig, Affine Hecke algebras and their graded version, J. Amer. Math. Soc. 2 (1989), no. 3, 599–635.
Mathematical Reviews (MathSciNet): MR90e:16049
Zentralblatt MATH: 0715.22020
Digital Object Identifier: doi:10.2307/1990945
[12] I. G. MacDonald, A new class of symmetric functions, Actes Séminaire Lotharingien, Publ. Inst. Rech. Math. Adv., Strasbourg, 1988, pp. 131–171.
[13] I. G. Macdonald, Affine Hecke algebras and orthogonal polynomials, Astérisque (1996), no. 237, Exp. No. 797, 4, 189–207, Séminaire Bourbaki, 47 (1994-95).
Mathematical Reviews (MathSciNet): MR99f:33024
Zentralblatt MATH: 0883.33008
[14] K. Mimachi, Connection problem in holonomic $q$-difference system associated with a Jackson integral of Jordan-Pochhammer type, Nagoya Math. J. 116 (1989), 149–161.
Mathematical Reviews (MathSciNet): MR91b:33023
Zentralblatt MATH: 0688.39002
Project Euclid: euclid.nmj/1118781433
[15] K. Mimachi and Y. Yamada, Singular vectors of the Virasoro algebra in terms of Jack symmetric polynomials, Comm. Math. Phys. 174 (1995), no. 2, 447–455.
Mathematical Reviews (MathSciNet): MR96m:17045
Zentralblatt MATH: 0842.17045
Digital Object Identifier: doi:10.1007/BF02099610
Project Euclid: euclid.cmp/1104275301
[16] K. Mimachi and Y. Yamada, Singular vectors of Virasoro algebra in terms of Jack symmetric polynomials, Sūrikaisekikenkyūsho Kōkyūroku (1995), no. 919, 68–78.
Mathematical Reviews (MathSciNet): MR1388327
Zentralblatt MATH: 0900.17008
[17] T. Ōshima and H. Sekiguchi, Commuting families of differential operators invariant under the action of a Weyl group, J. Math. Sci. Univ. Tokyo 2 (1995), no. 1, 1–75.
Mathematical Reviews (MathSciNet): MR96k:35006
Zentralblatt MATH: 0863.43007
[18] A. N. Varchenko and V. O. Tarasov, Jackson integral representations of solutions of the quantized Knizhnik-Zamolodchikov equation, St. Petersburg Math. J. 6 (1975), 275–313.
Zentralblatt MATH: 0824.33012
Mathematical Reviews (MathSciNet): MR1290820

2012 © Duke University Press

Duke Mathematical Journal

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?