Table of Contents
Modified symmetric group
A modified symmetric group is any member of a certain sequence 
of classical orthogonal matrix groups.
Definition
As a matrix group
For every 
the modified symmetric group for dimension 
is the subgroup of the general linear group 
given by all permutation 
-matrices multiplied by a factor of 
or 
, i.e., the set
where 
.
As a direct product
The modified symmetric group for dimension , where , can also be defined as the direct product of groups 
of the cyclic group 
of order 
and the symmetric group for dimension .
Basic properties
The modified symmetric groups are an 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 the category of partitions of even size that induces the corepresentation categories of . Its canonical generating set of partitions is 
.
Representation theory
Cohomology
Related quantum groups
References
