The symmetry group of a finite frame
Richard Vale and Shayne Waldron
Abstract:
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
tight frames.
Keywords:
finite frame,
geometrically uniform frame,
Gramian matrix,
harmonic frame,
maximally symmetric frames
partition frames,
symmetry group,
tight frame,
Math Review Classification:
Primary 42C15, 58D19;
Secondary 42C40, 52B15
Length: 17 pages
Last Updated: 17 September 2009
Availability: