Geodesic
Unitary integrals and related matrix models
Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 1, pp. 3-40

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We briefly review the basic properties of unitary matrix integrals, using three matrix models to analyze their properties: the ordinary unitary, the Brezin–Gross–Witten, and the Harish-Chandra–Itzykson–Zuber models. We especially emphasize the nontrivial aspects of the theory, from the De Wit–t'Hooft anomaly in unitary integrals to the problem of calculating correlators with the Itzykson–Zuber measure. We emphasize the method of character expansions as a technical tool. Unitary integrals are still insufficiently investigated, and many new results should be expected as this field attracts increased attention.
Keywords: matrix model, unitary group. 
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     author = {A. Yu. Morozov},
     title = {Unitary integrals and related matrix models},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     url = {http://geodesic.mathdoc.fr/item/TMF_2010_162_1_a0/}
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A. Yu. Morozov. Unitary integrals and related matrix models. Teoretičeskaâ i matematičeskaâ fizika, Tome 162 (2010) no. 1, pp. 3-40. http://geodesic.mathdoc.fr/item/TMF_2010_162_1_a0/