Frame vector multipliers for finite group representations

A frame vector (or generator) for a group representation π of a countable or finite group G on a Hilbert space H is a vector ξ∈H such that {π(g)ξ}g∈G is a Parseval frame for H. Frame vector multipliers are the unitary operators on H that map frame vectors to frame vectors. Based on a characterization of frame vectors with respect to the standard decomposition of a group representation as the direct sums of irreducible subrepresentations (with multiplicity), we obtain explicit characterizations of frame generator multipliers for two basic cases for finite group representations. With the help of these characterizations we obtain some necessary conditions of frame vector multipliers for general frame representations, and present several examples to demonstrate how these results can be used to get explicit characterizations for frame vector multipliers.