Titlebook: ICM-90 Satellite Conference Proceedings; Special Functions Masaki Kashiwara,Tetsuji Miwa Conference proceedings 1991 Springer-Verlag Tokyo

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Supernumary Polylogarithmic Ladders and Related Functional Equations,As discussed in several recent papers. the polylogarithmic function of order n and argument z can be defined through the series . It satisfies the recursion formula . and this, together with the elementary relation . extends the definition throughout the complex z-plane.

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The Chiral Potts Model: from Physics to Mathematics and back,We review the physics and mathematics of the chiral Potts spin chain with particular emphasis on computation of the energy levels by means of the solution of functional equations. We discuss in detail the relation of the integrable to the superintegrable case and the construction of the ground state in the massless level crossing regime.

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Hypergeometric Functions, Toric Varieties and Newton Polyhedra,briefly discuss main features of the classical Gauss function F(x)= .F. (a,b;c;x). By definition, F(x) is the solution of the hypergeometric equation . regular at x=0 and normalized by F(0)=1. Here a,b and c are complex parameters.

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On Some Properties of Robinson-Schensted Correspondence,nsted correspondence are presented. The results are based on the theory of rigged and filled configurations. We give the explicit description of the first tableaux of the filled configuration for Young tableaux . (or .) in terms of the structure of descents of the corresponding permutation.

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An Infinitesimally Quasi Invariant Measure on the Group of Diffeomorphisms of the Circle,ms therefore very doubtfull. The case of the group of the diffeomorphisms of the circle S. is quite different. We shall in this paper identify it with a loop space which carries a natural Wiener measure.

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978-4-431-70085-2Springer-Verlag Tokyo 1991

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https://doi.org/10.1007/978-4-431-68170-0Eigenvalue; Hypergeometric function; differential equation; distribution; logarithm; orthogonal polynomia