The construction of G-invariant finite tight frames

Richard Vale and Shayne Waldron


We give a complete classification of the finite tight frames which are $G$--invariant, i.e., invariant under the unitary action of group $G$. This result is constructive, and we use it to consider a number of examples. In particular, we determine the minimum number of generators for a tight frame for the orthogonal polynomials on an $n$--gon or cube, which is invariant under the symmetries of the weight.

Keywords: Finite tight frame, $G$--invariant frame, group frame, harmonic frame, group representation, linear action, complex reflection group, orthgonal polynomials on a regular polygon, orthgonal polynomials on a cube,

Math Review Classification: Primary 13A50, 33C52, 42C05, 42C15; Secondary 41A10, 52B11, 52B15

Length: 23 pages

Last Updated: 20 January 2015