New Trends in Quantum Integrable Systems: Proceedings of the Infinite Analysis 09

by Feigin, Boris; Jimbo, Michio; Okado, Masato

• ISBN13: 9789814324366
• ISBN10: 9814324361
• Format: Hardcover
• Copyright: 2010-11-30
• Publisher: World Scientific Pub Co Inc

Summary

The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009. As a continuation of the RIMS Research Project "Method of Algebraic Analysis in Integrable Systems" in 2004, the workshop's aim was to cover exciting new developments that have emerged during the recent years. Collected here are research articles based on the talks presented at the workshop, including the latest results obtained thereafter. the subjects discussed range across diverse areas such as correlation functions of solvable models, integrable models in quantum field theory, conformal field theory, mathematical aspects of Bethe ansatz, special functions and integrable differential/difference equations, representation theory of infinite dimensional algebras, integrable models and combinatorics. Through these topics, the reader is exposed to the most recent developments in the field of quantum integrable systems and related areas of mathematical physics.

Table of Contents

Preface	p. ix
Workshop program	p. xi
List of participants	p. xiii
Properties of linear integral equations related to the six-vertex model with disorder parameter	p. 1
Algebraic aspects of the correlation functions of the integrable higher-spin XXZ spin chains with arbitrary entries	p. 11
Characters of coinvariants in (1,p) logarithmic models	p. 35
XXZ scalar products, Miwa variables and discrete KP	p. 61
Quantum spin chains at finite temperatures	p. 81
Tropical spectral curves, Fay's trisecant identity, and generalized ultradiscrete Toda lattice	p. 101
On one-point functions of descendants in sine-Gordon model	p. 117
Perfect crystals for the quantum affine algebra Uq(C(1)n)	p. 139
Boundary quantum Knizhnik-Zamolodchikov equation	p. 157
A pentagon of identities, graded tensor products, and the Kirillov-Reshetikhin conjecture	p. 173
TBA for the Toda chain	p. 195
Generalized energies and integrable D(1)n cellular automaton	p. 221
Dyson's constant for the hypergeometric kernel	p. 243
Representation theory of a small ramified partition algebra	p. 269
The saga of the Ising susceptibility	p. 287
Bethe algebra of the glN+1 Gaudin model and algebra of functions on the critical set of the master function	p. 307
T-systems, Y-systems, and cluster algebras: Tamely laced case	p. 325
Periodic Benjamin-Ono equation with discrete Laplacian and 2D-Toda Hierarchy	p. 357
KP and Toda tau functions in Bethe ansatz	p. 373
Introduction to middle convolution for differential equations with irregular singularities	p. 393
Differential equations compatible with boundary rational qKZ equation	p. 421
Classification of solutions to the reflection equation for the critical ZN-symmetric vertex model I	p. 451
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