Integration over quantum permutation groups

Abstract

We find a combinatorial formula for the Haar measure of quantum permutation groups. This leads to a dynamic formula for laws of diagonal coefficients, explaining the Poisson/free Poisson convergence result for characters.

15 pages

References in corpus (2)

• Moments and Cumulants of Polynomial random variables on unitary groups, the Itzykson-Zuber integral and free probability
• Spectral measures of small index principal graphs

Cited by in corpus (23)

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• Modelling questions for quantum permutations
• Spectral analysis of the free orthogonal matrix
• Quantum permutation groups: a survey
• Moment Methods on compact groups: Weingarten calculus and its applications
• Classification results for easy quantum groups
• Existence and rigidity of quantum isometry groups for compact metric spaces
• Matrix Units in the Symmetric Group Algebra, and Unitary Integration
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• Reduktionssysteme zur Berechnung einer Auflösung der orthogonalen freien Quantengruppen $A_o(n)$
• On the problem of classifying simple compact quantum groups
• Duals of finite quantum permutation groups
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• Algebraic invariants of truncated Fourier matrices
• Linear algebra and group theory