category_of_two-colored_pair_partitions
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Category of two-colored pair partitions
The category of two-colored pair partitions is a category of two-colored partitions inducing the co-representation categories of the orthogonal groups.
Definition
By the category of two-colored pair partitions one denotes the subcategory of the category of all two-colored partitions 
whose morphism class is the set of all pair partitions. It was introduced by Tarrago and Weber in [TaWe18], Theorem 8.3 under the name 
.
- A two-colored partition
is called a pair partition (see category of all pair partitions in the uncolored case), if every block 
of 
satisfies 
. - The name set of all pair partitions partitions with neutral blocks is to be taken literally.
The set of two-colored pair partitions is the morphism set of the subcategory of generated by the set 
.
Associated unitary easy quantum groups
The category of two-colored pair partitions induces the co-representation categories of the orthogonal groups 
.
References
[TaWe18]
Tarrago, Pierre and Weber, Moritz, February 2018. The classification of tensor categories of two-colored non-crossing partitions. Journal of Combinatorial Theory, Series A, 154, pp.464–506.
category_of_two-colored_pair_partitions.txt · Last modified: 2021/11/23 11:56 (external edit)
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