Mathphys Odyssey 2001

by Kashiwara, Masaki; Miwa, Tetsuji

• ISBN13: 9780817642600
• ISBN10: 0817642609
• Format: Hardcover
• Copyright: 2002-06-01
• Publisher: Birkhauser

Summary

Developments in mathematical physics during the second half of the 20th century influenced a number of mathematical areas, among the more significant being representation theory, differential equations, combinatorics, and algebraic geometry. In all of them, the dynamic role of integrable models has been central, largely due to two essential properties: the fact that integrable models possess infinite degrees of freedom and infinite dimensional symmetries. This volume focuses on the ongoing importance of integrability in covering the following topics: conformal field theory, massive quantum field theory, solvable lattice models, quantum affine algebras, the Painlevè equations and combinatorics. Contributors: H. Au-Yang, R.J. Baxter, H.E. Boos, E. Date, K. Fabricius, V.A. Fateev, B. Feigin, G.Hatayama, A. Its, M. Jimbo, A. Kapaev, A.N. Kirillov, V.E. Korepin, A.Kuniba, J.M. Maillet, B.M. McCoy, C. Mercat, T. Miwa, A. Nakayashiki, M.Okado, C.H.Otto Chui, P.A. Pearce, J.H.H. Perk, V. Petkova, A. Schilling, F.A. Smirnov, T.Takagi, Y. Takeyama, M. Taneda, C.A. Tracy, Z.Tsuboi, H. Widom, J.-B. Zuber 'MathPhys"Odyssey 2001" will serve as an excellent reference text for mathematical physicists and graduate students in a number of areas.

Table of Contents

Preface	ix
Wavevector-Dependent Susceptibility in Aperiodic Planar Ising Models	1	(22)
H. Au-Yang
J.H.H. Perk
Correlation Functions and Susceptibility in the Z-Invariant Ising Model	23	(26)
H. Au-Yang
J.H.H. Perk
A Rapidity-Independent Parameter in the Star-Triangle Relation	49	(16)
R. J. Baxter
Evaluation of Integrals Representing Correlations in the XXX Heisenberg Spin Chain	65	(44)
H. E. Boos
V.E. Korepin
A Note on Quotients of the Onsager Algebra	109	(10)
E. Date
Evaluation Parameters and Bethe Roots for the Six-Vertex Model at Roots of Unity	119	(26)
K. Fabricius
B.M. McCoy
Normalization Factors, Reflection Amplitudes and Integrable Systems	145	(34)
V.A. Fateev
Vertex Operator Algebra Arising from the Minimal Series M(3, p) and Monomial Basis	179	(26)
B. L. Feigin
M. Jimbo
T. Miwa
Paths, Crystals and Fermionic Formulae	205	(68)
G. Hatayama
A. Kuniba
M. Okado
T. Takagi
Z. Tsuboi
The Nonlinear Steepest Descent Approach to the Asymptotics of the Second Painleve Transcendent in the Complex Domain	273	(40)
A. R. Its
A. A. Kapaev
Generalized Umemura Polynomials and the Hirota-Miwa Equation	313	(20)
A. N. Kirillov
M. Taneda
Correlation Functions of Quantum Integrable Models: The XXZ Spin Chain	333	(24)
J. M. Maillet
On Form Factors of the SU(2) Invariant Thirring Model	357	(34)
A. Nakayashiki
Y. Takeyama
Integrable Boundaries and Universal TBA Functional Equations	391	(24)
C. H. Otto Chui
C. Mercat
P. A. Pearce
Conformal Field Theories, Graphs and Quantum Algebras	415	(22)
V. Petkova
J.-B. Zuber
g-Supernomial Coefficients: From Riggings to Ribbons	437	(18)
A. Schilling
Separation of Variables for Quantum Integrable Models Related to Uq (slN)	455	(12)
F. A. Smirnov
On a Distribution Function Arising in Computational Biology	467
C. A. Tracy
H. Widom