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

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. (C) 2002 Wiley Periodicals. Inc.