Unitary quantum groups vs quantum reflection groups

Abstract

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 $H_N^{[\infty ]}=<H_N,T_N^{+}>$, 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.

Withdrawn by the author - the main findings in this paper are now part of arXiv:1909.08152

References in corpus (3)

• Categories of Two-Colored Pair Partitions, Part II: Categories Indexed by Semigroups
• The intertwiner spaces of non-easy group-theoretical quantum groups
• Unitary easy quantum groups: geometric aspects

Cited by in corpus (1)

• Hopf algebras with enough quotients