CONTENTS -- Preface -- Monodromy Problem Related to Wu-Sutherland Equations -- 1 Local Solutions to Wu-Sutherland Equations -- 2 The analytic continuation and the monodromy problem -- References -- A Remark on the Harish-Chandra Series for Hyperboloids -- References -- Quantum Integrable Lattice Field Theory and Quantum Dilogarithm Function -- 1 Introduction -- 2 Quantum Dilogarithm Function I -- 3 Lattice SG System -- 4 Affine Toda Lattice Field Theory -- 5 Quantum Dilogarithm Function II -- 6 Lattice SG System Revisited -- 7 Dual Affine Toda Lattice System -- 8 Concluding Remarks -- Acknowledgement -- References -- A Theory of Interacting Many-Body Systems with Exclusion Statistics: Origin of Exclusion Statistics Haldane Liquids. Sutherland-Wu Equations Grand Partition Function and Lee-Yang Theorem -- 1 Introduction -- 2 Origin of Exclusion statistics -- 3 Haldane liquids -- 4 Sutherland-Wu equations -- 5 Basic Properties of the Haldane Liquid -- 6 Thermodynamics and the Cluster Expansions -- 7 Grand Partition Function -- 8 Grand Partition Function in the Momentum Representation -- 9 Lee-Yang Theorem -- 10 Duality -- 11 conclusion -- Acknowledgments -- References -- Symmetric Spaces over Finite Fields Frobenius-Schur Indices and Symmetric Function Identities -- 1 Introduction -- 2 Frobenius character formula and its variations -- 3 Finite symmetric spaces and Hall-Littlewood symmetric functions -- 4 Symmetric groups -- 5 Imprimitive complex reflection groups -- 6 Inner products -- References -- Ubiquity of Kostka Polynomials -- 1 Introduction -- 2 Kostka-Foulkes polynomials and weight multiplicities -- 3 Parabolic Kostka polynomials -- 4 Fermionic formula for parabolic Kostka polynomials -- 5 Generalized exponents and mixed tensor representations -- 6 Internal product of Schur functions -- 7 Liskova semigroup.

8 Stable behavior of Kostka-Foulkes polynomials -- References -- Transformations of U(n + 1) Multiple Basic Hypergeometric Series -- 1 Introduction -- 2 Background and notation -- 3 A U(n + 1) extension of the g-binomial theorem -- 4 U(n + 1) extensions of the 60s summation theorem -- 5 Definitions of An Cn and Dn multiple q-series -- 6 The U(n + 1) (matrix) Bailey Transform -- 7 The U(n + 1) Bailey Lemma -- 8 The U(n + 1) (classical) Bailey Transform -- 9 A U(n + 1) extension of the 10O9 transformation -- 10 New infinite families of eta function identities -- 11 New formulas for 16 and 24 squares -- References -- Kashaev's Invariant and the Volume of a Hyperbolic Knot after Y. Yokota -- 1 Introduction -- 2 Algebra -- 3 Geometry -- 4 Analysis and Harmony -- References -- Integral Solutions of Hypergeometric g-Difference Systems with

Representation of Umemura Polynomials for the Sixth Painleve Equation by the Generalized Jacobi Polynomials -- 1 Introduction -- 2 Some Propositions -- 3 Auxiliary lemmas -- 4 Proof of Theorem 1 -- References -- Two Relations that Generalize the g-Serre Relations and the Dolan-Grady Relations -- 1 Leonard pairs -- 2 Tridiagonal pairs -- 3 Tridiagonal pairs in representation theory -- 4 The parameter sequence and the eigenvalues -- 5 Infinite dimensional modules for Tridiagonal algebras -- References.