The radial MASA in free orthogonal quantum groups
Amaury Freslon, Roland Vergnioux
TL;DR
This paper demonstrates that the radial subalgebra in free orthogonal quantum group factors is maximal abelian and mixing, providing new insights into their structure through properties of Jones-Wenzl projections.
Contribution
It introduces novel properties of Jones-Wenzl projections and estimates scalar products of irreducible representation coefficients to analyze the radial subalgebra.
Findings
Radial subalgebra is maximal abelian
Radial subalgebra exhibits mixing properties
Computed the associated bimodule structure
Abstract
We prove that the radial subalgebra in free orthogonal quantum group factors is maximal abelian and mixing, and we compute the associated bimodule. The proof relies on new properties of the Jones-Wenzl projections and on an estimate of certain scalar products of coefficients of irreducible representations.
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