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.
Monodromy problem related to Wu-Sutherland equations, K. Aomoto; quantum integrable lattice field theory and quantum dilogarithm function, K. Hirami; symmetric spaces over finite fields, Frobenius-Schur indices, and symmetric function identities, N. Kawanaka; uniquity of Kostka polynomials, A.N. Kirillov; transformations of "U"(n+1) multiple basic hypergeometric series, S.C. Milne; Kashaev's invariant and the volume of a hyperbolic knot after Y. Yokota, H. Murakami; birational Weyl group action arising from a nilpotent Poisson algebra, M. Noumi and Y. Yamada; two relations that generalize the "q"-Serre relations and the Dolan-Grady relations, P. Terwilliger. (Part contents).