February Fourier Talks 2016

There is an abstract version of the Gabor systems duality principle for group rep- resentations, and it is known that this duality principle has some connections with the classification problem for free-group von Neumann algebras. In this talk I will revisit this general duality principle, and discuss some recent both trivial and nontrivial observations that lead to a generalization of the Wexler-Raz biorthogonality and the Fundamental Identity for Gabor representations to general group representations. Additionally, I will also discuss a duality principle connecting the "super-frames" and "muti-frames" through a commutant dual pair of group representations (which might be already known for Gabor representations).