Abstract
We present several formulae for Selberg-type integrals associated with the Lie algebra \(\mathfrak{s}\mathfrak{l}_3\).
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References
Aomoto, K.: Jacobi polynomials associated with Selberg integrals, SIAM J. Math. Anal. 18 (1987), 545–549.
Aomoto, K.: On the complex Selberg integral, Quart. J. Math. Oxford 38 (1987), 385–399.
Aomoto, K. and Kato, Y.: Gauss decomposition of connection matrices for symmetric A-type Jackson integrals, Selecta Math., NS 1(4) (1995), 623–666.
Askey, R.: Some basic hypergeometric extensions of integrals of Selberg and Andrews, SIAM J. Math. Anal. 11 (1980), 938–951.
Dotsenko, V.: Solving the SU(2) conformal eld theory with the Wakimoto free-eld representation (in Russian) (1990), 1–31.
Dotsenko, V. and Fateev, V.: Conformal algebra and multi-point correlation functions in 2-D statistical models, Nuclear Phys. B 240 (1984), 312–348.
Dotsenko, V. and Fateev, V.: Four-point correlation functions and the operator algebra in 2-D conformal invariant theories with central charge C ⩽ 1, Nuclear Phys. B 251 (1985), 691–734.
Etingof, P., Frenkel, I. and Kirillov, A. Jr.: Lectures on Representation Theory and Knizhnik Zamolodchikov Equations, Math. Surveys Monogr. 58, Amer. Math. Soc., Providence, RI, 1998.
Etingof, P. and Varchenko, A.: Dynamical Weyl groups and applications, Adv. Math. 167(1) (2002), 74–127.
Felder, G., Markov, Ya., Tarasov, V. and Varchenko, A.: Differential equations compatible with KZ equations, Math. Phys. Anal. Geom. 3 (2000), 139–177.
Felder, G., Stevens, L. and Varchenko, A.: Elliptic Selberg integrals and conformal blocks, Preprint (2002), 1–13 math.QA/0210040.
Felder, G. and Varchenko, A.: Integral representations for solutions of the elliptic Knizhnik-Zamolodchikov-Bernard equation, Internat. Math. Res. Notices 5 (1995), 221–233.
Knizhnik, V. and Zamolodchikov, A.: Current algebra and Wess-Zumino model in two dimensions, Nuclear Phys. B 247 (1984), 83–103.
Macdonald, I. G.: Some conjectures for root systems, SIAM J. Math. Anal. 13 (1982), 988–1007.
Mehta, M. L.: Random Matrices, Academic Press, New York, 1991.
Markov, Ya. and Varchenko, A.: Solutions of trigonometric KZ equations satisfy dynamical difference equations, Adv. Math. 166(1) (2002), 100–147.
Mukhin, E. and Varchenko, A.: Remarks on critical points of phase functions and norms of Bethe vectors, Adv. Stud. Pure Math. 27 (2000), 239–246.
Selberg, A.: Bemerkninger om et multiplet integral, Norsk Mat. Tidsskr. 26 (1944), 71–78.
Schechtman, V. V. and Varchenko, A. N.: Arrangements of hyperplanes and Lie algebras homology, Invent. Math. 106 (1991), 139–194.
Tarasov, V. and Varchenko, A.: Geometry of q-hypergeometric functions as a bridge between Yangians and quantum affine algebras, Invent. Math. 128(3) (1997), 501–588.
Tarasov, V. and Varchenko, A.: Difference equations compatible with trigonometric KZ differential equations, Internat. Math. Res. Notices 15 (2000), 801–829.
Tarasov, V. and Varchenko, A.: Duality for Knizhnik Zamolodchikov and dynamical equations, Acta Appl. Math. 73 (2002), 141–154.
Varchenko, A.: Multidimensional Hypergeometric Functions and Representation Theory of Lie Algebras and Algebras and Quantum Groups, Adv. Ser. Math. Phys. 21, World Scientific, Singapore, 1995.
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Tarasov, V., Varchenko, A. Selberg-Type Integrals Associated with SL3 . Letters in Mathematical Physics 65, 173–185 (2003). https://doi.org/10.1023/B:MATH.0000010712.67685.9d
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DOI: https://doi.org/10.1023/B:MATH.0000010712.67685.9d