Expansion of polynomial Lie group integrals in terms of certain maps on surfaces, and factorizations of permutations

Marcel Novaes

doi:10.1088/1751-8121/aa55f2

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arXiv · 1601.08206

Expansion of polynomial Lie group integrals in terms of certain maps on surfaces, and factorizations of permutations

Marcel Novaes

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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.

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Marcel Novaes. 2016-02-07. Expansion of polynomial Lie group integrals in terms of certain maps on surfaces, and factorizations of permutations. https://doi.org/10.1088/1751-8121%2Faa55f2

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