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higher_hyperoctahedral_series [2020/02/07 06:27] amang [Basic Properties]		higher_hyperoctahedral_series [2021/11/23 11:56] (current)
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-	For every $s\in \N$ with $s\geq 3$ the quantum groups $(H_N^{[s]})_{N\in \N}$ of the higher hyperoctahedral series with parameter $s$ are an [[easy_quantum_group\|easy]] family of compact matrix quantum groups, i.e., the intertwiner spaces of their corepresentation categories are induced by a [[category of partitions]]. More precisely, it is a [[group-theoretical hyperoctahedral categories of partitions\|group-theoretical hyperoctahedral category of partitions]] that induces the corepresentation categories of $(H_N^{[s]})_{N\in \N}$. Canonically, if $s<\infty$, it is generated by $h_s$ [(:ref:RaWe14)], the partition whose [[partition#word_representation\|word representation]] is given by $(ab)^s$. See also [[categories of the higher hyperoctahedral series]]. The corepresentation categories of $(H_N^{[\infty]})_{N\in\N}$ are induced by $\Paabaab$.	+	For every $s\in \N$ with $s\geq 3$ the quantum groups $(H_N^{[s]})_{N\in \N}$ of the higher hyperoctahedral series with parameter $s$ are an [[easy_quantum_group\|easy]] family of compact matrix quantum groups, i.e., the intertwiner spaces of their corepresentation categories are induced by a [[category of partitions]]. More precisely, it is a [[group-theoretical hyperoctahedral categories of partitions\|group-theoretical hyperoctahedral category of partitions]] that induces the corepresentation categories of $(H_N^{[s]})_{N\in \N}$. Canonically, if $s<\infty$, it is generated by $h_s$ [(:ref:RaWe14)], the partition whose [[partition#word_representation\|word representation]] is given by $(\mathsf{ab})^s$. See also [[categories of the higher hyperoctahedral series]]. The corepresentation categories of $(H_N^{[\infty]})_{N\in\N}$ are induced by $\Paabaab$.

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