In 2007, Professor Akihiro Tsuchiya of Nagoya University reached the retirement age of sixty-three. He has played a significant role in mathematical physics over the decades, most particularly in the foundation of conformal field theory, which was the first nontrivial example of a mathematically rigorous quantum field theory.

This volume contains the proceedings of the international conference on the occasion of his retirement. Included are conformal field theories and related topics such as solvable statistical models, representation theory of affine algebras, monodromy preserving deformations, and string theories. Readers interested in these subjects will find exciting and stimulating insights and questions from these articles.

Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS.

Readership

Graduate students and researchers interested in conformal field theories, representation theory of affine algebras, monodromy preserving deformations, and string theories.

Table of Contents

• K. Nagatomo and A. Tsuchiya -- The triplet vertex operator algebra \(W(p)\) and the restricted quantum group \(\bar{U}_q(sl_2)\) at \(q=e^{\pi i/p}\)
• T. Arakawa -- Representation theory of W-algebras, II
• V. V. Bazhanov -- Chiral Potts model and the discrete Sine-Gordon model at roots of unity
• T. Eguchi, Y. Sugawara, and A. Taormina -- Modular forms and elliptic genera for ALE spaces
• B. Feigin, E. Feigin<, and I. Tipunin -- Fermionic formulas for characters of \((1,p)\) logarithmic model in \(\Phi_{2,1}\) quasiparticle realisation
• B. Feigin and E. Frenkel -- Quantization of soliton systems and Langlands duality
• K. Hasegawa -- Quantizing the Bäcklund transformations of Painlevé equations and the quantum discrete Painlevé VI equation
• G. Kuroki -- Quantum groups and quantization of Weyl group symmetries of Painlevé systems
• W. Nakai and T. Nakanishi -- On Frenkel-Mukhin algorithm for \(q\)-character of quantum affine algebras
• H. Nakajima and K. Yoshioka -- Perverse coherent sheaves on blow-up. I. A quiver description
• K. Takasaki -- Differential Fay identities and auxiliary linear problem of integrable hierarchies