MathPhys Odyssey 2001

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 Painlevé 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.

'MathPhys Odyssey 2001' will serve as an excellent reference text for mathematical physicists and graduate students in a number of areas.; Kashiwara/Miwa have a good track record with both SV and Birkhauser.

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 areas, the dynamic role of integrable models has been central. This volume focuses on the ongoing importance of integrability in: conformal field theory, massive quantum field theory, solvable lattice models, quantum affine algebras, the Painlevé equations and combinatorics. Will serve as an excellent reference text for mathematical physicists and graduate students.

Wavevector-Dependent Susceptibility in Aperiodic Planar Ising Models.- Correlation Functions and Susceptibility in the Z-Invariant Ising Model.- A Rapidity-Independent Parameter in the Star-Triangle Relation.- Evaluation of Integrals Representing Correlations in the XXX Heisenberg Spin Chain.- A Note on Quotients of the Onsager Algebra.- Evaluation Parameters and Bethe Roots for the Six-Vertex Model at Roots of Unity.- Normalization Factors, Reflection Amplitudes and Integrable Systems.- Vertex Operator Algebra Arising from the Minimal Series M(3, p)and Monomial Basis.- Paths, Crystals and Fermionic Formulae.- The Nonlinear Steepest Descent Approach to the Asymptotics of the Second Painlevé Transcendent in the Complex Domain.- Generalized Umemura Polynomials and the Hirota-Miwa Equation.- Correlation Functions of Quantum Integrable Models: The XXZ Spin Chain.- On Form Factors of the SU(2) Invariant Thirring Model.- Integrable Boundaries and Universal TBA Functional Equations.- Conformal Field Theories, Graphs and Quantum Algebras.- q-Supernomial Coefficients: From Riggings to Ribbons.- Separation of Variables for Quantum Integrable Models Related to $${U_q}({widehat {sl}_N})$$.- On a Distribution Function Arising in Computational Biology.