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This volume contains research and review papers on different branches of mathematics and mathematical physics, written by the leading specialists. Among the contributed papers are articles on: (i) multiple basic hypergeometric functions with applications to the number theory, (ii) birational representations of affine Weyl groups with applications to discrete integrable systems, (iii) algebraic geometry and Painleve VI, and (iv) combinatorics of Kostka-Foulkes polynomials.

The Nagoya 2000 International Workshop gathered together a group of scientists actively working in combinatorics, representation theory, special functions, number theory and mathematical physics, to acquaint the participants with some basic results in these fields and to discuss existing and possible interactions between the mentioned subjects. This volume constitutes the proceedings of the workshop.