The symmetry group of a finite frame
Richard Vale and Shayne Waldron
We define the symmetry group of a finite frame
as a group of permutations on its index set.
This group is closely related to the symmetry group of [VW05]
for tight frames:
they are isomorphic when the frame is tight and has distinct vectors.
The symmetry group is the same for all similar frames,
in particular for a frame, its dual and canonical tight frames.
It can easily be calculated from the Gramian matrix of the
canonical tight frame.
Further, a frame and its complementary frame have the
same symmetry group. We exploit this last property to
construct and and classify some classes of highly symmetric
geometrically uniform frame,
maximally symmetric frames
Math Review Classification:
Primary 42C15, 58D19;
Secondary 42C40, 52B15
Length: 17 pages
Last Updated: 17 September 2009