Expansion of polynomial Lie group integrals in terms of certain maps on surfaces, and factorizations of permutations. (12th January 2017)

• Record Type: Journal Article
• Authors: Novaes, Marcel
• Is Part Of: Journal of physics. Volume 50:Number 7(2017)
• Publication Date: 2017-01-12
• Subjects: Lie groups -- quantum chaos -- maps on surfaces -- factorizations of permutations; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa55f2
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: Using the diagrammatic approach to integrals over Gaussian random matrices, we find a representation for polynomial Lie group integrals as infinite sums over certain maps on surfaces. The maps involved satisfy a specific condition: they have some marked vertices, and no closed walks that avoid these vertices. We also formulate our results in terms of permutations, arriving at new kinds of factorization problems.