by Arkady Berenstein (University of Oregon, USA), David Kazhdan (Hebrew University, Israel), Cédric Lecouvey (Laboratoire de Mathematiques Joseph Liouville, France), Masato Okado (Osaka University, Japan), Anne Schilling (University of California, USA), Taichiro Takagi (National Defense Academy, Japan), & Alexander Veselov (Loughborough University, Russia)

This volume is a collection of six papers based on the expository lectures of the workshop “Combinatorial Aspect of Integrable Systems” held at RIMS during July 26–30, 2004, as a part of the Project Research 2004 “Method of Algebraic Analysis in Integrable Systems”. The topics range over crystal bases of quantum groups, its algebra–geometric analogue known as geometric crystal, generalizations of Robinson–Schensted type correspondence, fermionic formula related to Bethe ansatz, applications of crystal bases to soliton celluar automata, Yang–Baxter maps, and integrable discrete dynamics. All the papers are friendly written with many illustrative examples and intimately related to each other. This volume will serve as a good guide for researchers and graduate students who are interested in this fascinating subject.

Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets

• Lecture Notes on Geometric Crystals and Their Combinatorial Analogues
• Combinatorics of Crystal Grraphs for the Root Systems of Types A_n, B_n, C_n, D_n and G₂X=M Conjecture
• X=M Theorem: Fermionic Formulas and Rigged Configurations under Review
• Soliton Cellular Automata
• Yang–Baxter Maps: Dynamical Point of View