Fredholm determinants, Jimbo‐Miwa‐Ueno τ‐functions, and representation theory

Abstract

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 Painlevé equations. Their methods are based on the theory of integrable operators and the theory of Riemann‐Hilbert problems. © 2002 Wiley Periodicals, Inc.