Integration over compact quantum groups

Abstract

We find a combinatorial formula for the Haar functional of the orthogonal and unitary quantum groups. As an application, we consider diagonal coefficients of the fundamental representation, and we investigate their spectral measures.

24 pages

References in corpus (6)

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Cited by in corpus (38)

• On some properties of orthogonal Weingarten functions
• The hyperoctahedral quantum group
• Integration over quantum permutation groups
• De Finetti theorems for easy quantum groups
• The Weingarten Calculus
• Integration over the Pauli quantum group
• Quantum isometries and noncommutative spheres
• Hochschild homology of Hopf algebras and free Yetter-Drinfeld resolutions of the counit
• Liberations and twists of real and complex spheres
• Spectral measures of small index principal graphs
• Free wreath product quantum groups : the monoidal category, approximation properties and free probability
• Monotone Hurwitz numbers and the HCIZ integral II
• The Connes embedding property for quantum group von Neumann algebras
• Jucys-Murphy Elements and Unitary Matrix Integrals
• Orthogonal free quantum group factors are strongly 1-bounded
• The orthogonal Weingarten formula in compact form
• Liberation of orthogonal Lie groups
• Free Analysis Questions II: The Grassmannian Completion and The Series Expansions at the Origin
• Study of quantum symmetries for vertex-transitive graphs using intertwiner spaces
• Strong asymptotic freeness for free orthogonal quantum groups
• Decomposition results for Gram matrix determinants
• Semisimplicity and Indecomposable Objects in Interpolating Partition Categories
• The full classification of orthogonal easy quantum groups
• Quantum groups and generalized circular elements
• Quantum Symmetries and Strong Haagerup Inequalities
• Spectral analysis of the free orthogonal matrix
• Quantum automorphism groups of vertex-transitive graphs of order $\le 11$
• Quantum permutation groups: a survey
• Moment Methods on compact groups: Weingarten calculus and its applications
• Strong 1-Boundedness of Unimodular Free Orthogonal Quantum Groups
• Cyclotomic expansion of exceptional spectral measures
• On the problem of classifying simple compact quantum groups
• Reduktionssysteme zur Berechnung einer Auflösung der orthogonalen freien Quantengruppen $A_o(n)$
• Graphs having no quantum symmetry
• The Haar State on SU_q(N)
• Asymptotic infinitesimal freeness with amalgamation for Haar quantum unitary random matrices
• A note on free quantum groups
• Principles of operator algebras