Functions and Analysis


Unitary Quantum Groups vs Quantum Reflection Groups

Authors: Teo Banica

We study the intermediate liberation problem for the real and complex unitary and reflection groups, namely $O_N,U_N,H_N,K_N$. For any of these groups $G_N$, the problem is that of understanding the structure of the intermediate quantum groups $G_N\subset G_N^\times\subset G_N^+$, in terms of the recently introduced notions of ``soft'' and ``hard'' liberation. We solve here some of these questions, our key ingredient being the generation formula $H_N^{[\infty]}=$, coming via crossed product methods. Also, we conjecture the existence of a ``contravariant duality'' between the liberations of $H_N$ and of $U_N$, as a solution to the lack of a covariant duality between these liberations.

Comments: 26 Pages.

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Submission history

[v1] 2019-04-21 10:18:41

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