2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56900The 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 pagesMathematical PhysicsClassical Analysis and ODEsRepresentation Theorytext