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arxiv: math-ph/0111007 · v1 · submitted 2001-11-05 · 🧮 math-ph · math.CA· math.MP· math.RT

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

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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.

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