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Easy unitary quantum group
Easy unitary quantum groups are a particular class of compact matrix quantum groups introduced by Freslon and Weber in [FreWeb16], generalizing the definition of easy orthogonal quantum groups given by Banica and Speicher in [BanSp09]. Every easy unitary quantum group is by definition a compact quantum subgroup of a free unitary quantum group.
Definition
Informally, a compact matrix quantum group is called easy unitary if it is a compact quantum subgroup of the corresponding free unitary quantum group and if its corepresentation category is generated by a category of partitions. Formally, for every 
, any compact 
-matrix quantum group 
is called an easy unitary quantum group if the corepresentation category 
of 
has as objects the set 
of tuples of arbitrary lengths with two distinct possible entries 
and 
and if there exists some category of two-colored partitions 
such that for all 
and all 
the morphism set 
of is given by
where for all 
the linear map 
satisfies for all 
,
where 
is the standard basis of 
and where for all 
the symbol 
is 
if the kernel, i.e., the induced partition with 
upper and 
lower points, of 
refines 
and is 
otherwise.
References
