Physics and combinatorics 1999 : procceedings [i.e. proceedings] of the Nagoya 1999 International Workshop, Graduate School of Mathematics, Nagoya University / editors, Anatol N. Kirillov, Akihiro Tsuchiya & Hiroshi Umemura.

Format:

Book

Conference/Event

Contributor:

Kirillov, Anatol N.

Tsuchiya, A. (Akihiro), 1943-

Umemura, Hiroshi, 1944-2019.

Conference Name:

International Workshop on Physics and Combinatorics (1st : 1999 : Nagoya University)

Language:

English

Subjects (All):

Combinatorial analysis--Congresses.

Combinatorial analysis.

Mathematical physics--Congresses.

Mathematical physics.

Statistical physics--Congresses.

Statistical physics.

Physical Description:

1 online resource (408 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, c2001.

Language Note:

English

Summary:

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. Contents: Monodromy Problem Related to Wu-Sutherland Equations (K Aomoto); Quantum Integrable Lattice Field Theory and Quan

Contents:

Preface; CONTENTS; 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 Theorem1 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 Identities1 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 functions7 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 squaresReferences; 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 |q| = 1; 1 Introduction; 2 Double Sine Function and a ""g-Shifted Factorial with |q|= 1""; 3 Integral Solutions of the Barnes Type; 4 Integral Solutions of the Euler Type; References; Birational Weyl Group Action Arising from a Nilpotent Poisson Algebra; Introduction; 1 Summary of results; 2 Examples of rank 2

3 Realization of Weyl groups

Notes:

Held August 23-27, 1999.

Includes bibliographical references.

ISBN:

9786611951719

9781281951717

1281951714

9789812810199

9812810196

OCLC:

879024828