Fredholm determinants, Jimbo-Miwa-Ueno tau-functions, and representation theory

Abstract

The authors show that a wide class of Fredholm determinants arising in the representation theory of "big" groups such as the infinite-dimensional unitary group, solve Painleve equations. Their methods are based on the theory of integrable operators and the theory of Riemann-Hilbert problems.

AMSTeX, 62 pages