Abstract
We consider several orthogonal quantum groups satisfying the “easiness” assumption axiomatized in our previous paper. For each of them we discuss the computation of the asymptotic law of Tr(u k) with respect to the Haar measure, u being the fundamental representation. For the classical groups O n , S n we recover in this way some well-known results of Diaconis and Shahshahani.
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Acknowledgements
The work of T.B. was supported by the ANR grants “Galoisint” and “Granma”, and the work of R.S. was supported by a Discovery grant from NSERC.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Banica, T., Curran, S. & Speicher, R. Stochastic aspects of easy quantum groups. Probab. Theory Relat. Fields 149, 435–462 (2011). https://doi.org/10.1007/s00440-010-0260-4
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DOI: https://doi.org/10.1007/s00440-010-0260-4