non-group-theoretical_hyperoctahedral_categories_of_partitions
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non-group-theoretical_hyperoctahedral_categories_of_partitions [2020/04/18 07:20] amang [Definition] |
non-group-theoretical_hyperoctahedral_categories_of_partitions [2021/11/23 11:56] (current) |
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| * where $Y_1$, $Y_2$ and $Y_3$ contain none of the letters $a_1,\ldots,a_k$. | * where $Y_1$, $Y_2$ and $Y_3$ contain none of the letters $a_1,\ldots,a_k$. | ||
| - | Any such partition is necessarily of [[category of partitions of even size|even size]] and has [[category of partitions with blocks of even size and even distances between legs|even distances between legs]]. Moreover, if $l\leq 1$, then it is also [[category of all non-crossing partitions|non-crossing]]. | + | Any such partition is necessarily of [[category of partitions of even size|even size]] and has [[category of partitions with blocks of even size and even distances between legs|parity-balanced legs]]. Moreover, if $l\leq 1$, then it is also [[category of all non-crossing partitions|non-crossing]]. |
| ===== Canonical Generator ===== | ===== Canonical Generator ===== | ||
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| ===== Associated easy quantum group ===== | ===== Associated easy quantum group ===== | ||
| - | Via [[tannaka_krein_duality|Tannaka-Krein duality]] for compact quantum groups, for every $l\in\N\cup\{\infty\}$ the non-group-theoretical hyperoctahedral category with parameter $l$ corresponds to a family of [[non-group-theoretical hyperoctahedral easy quantum group|non-group-theoretical hyperoctahedral easy quantum groups]]. | + | Via [[tannaka_krein_duality|Tannaka-Krein duality]] for compact quantum groups, for every $l\in\N\cup\{\infty\}$ the non-group-theoretical hyperoctahedral category with parameter $l$ corresponds to a family of [[non-group-theoretical_hyperoctahedral_easy_orthogonal_quantum_groups|non-group-theoretical hyperoctahedral easy quantum groups]]. |
| ===== References ===== | ===== References ===== | ||
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