Title of lectures
Algebraic analysis of solvable lattice models
Lecturer:
Tetsuji MIWA, RIMS, Kyoto University
Outline:
Algebraic analysis serves to study interesting and useful special functions
and the differential and difference equations satisfied by them by
algebraic methods. The importance of solvable lattice models lies in the
fact that they give non-trivial examples of systems of infinite degrees of
freedom than can be solved analytically. I will explain that the
solvability of the models is related to the hidden symmetries of the
system, which are infinite dimensional, and how to exploit these symmetries
to obtain the correlation functions and the form factors.
Lecture 1 - Solvable lattice models.
Introduction to solvability of lattice models including the commuting transfer
matrices, the Yang- Baxter equations and the corner transfer matrix method.
Lecture 2 - Affine quantum algebras.
Introduction to the infinite dimensional symmetries including the evaluation
modules, the highest weight representations and the vertex operators.
Lecture 3 - Diagonalization and correlation functions.
Solving solvable models by using the representation theory of the affine
quantum algebras, in particular, the bosonization.
Lecture 4 - Combinatorial aspects of the solvable lattice models.
Crystal basis and quasi-particle structure.
Lecture 5 - The qKZ equations.
Integral formulas for |q|=1.
References:
[1] Jimbo, M. and Miwa, T., Algebraic Analysis of Solvable Lattice Models,
CBMS Lecture Notes Series, 85, AMS, 1995.
[2] Baxter, R., Exactly Solved Models in Statistical Mechanics, Academic
Press, 1982.
[3] Kac, V., Infinite Dimensional Lie Algebras, Cambrige University Press,
Third edition, 1990.