Fredholm Determinants, Jimbo-Miwa-Ueno τ-Functions, and Representation Theory

Alexei Borodin, Percy Deift

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1160-1230
Number of pages71
JournalCommunications on Pure and Applied Mathematics
Volume55
Issue number9
DOIs
StatePublished - Sep 2002

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Fredholm Determinant
Representation Theory
Riemann-Hilbert Problem
Unitary group
Operator
Class

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Fredholm Determinants, Jimbo-Miwa-Ueno τ-Functions, and Representation Theory. / Borodin, Alexei; Deift, Percy.

In: Communications on Pure and Applied Mathematics, Vol. 55, No. 9, 09.2002, p. 1160-1230.

Research output: Contribution to journalArticle

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