Collaborative Research: An Analysis of Characters and Matrix Coefficients for Representations of Real Classical Lie Groups

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AbstractPrzebindaThe aim of this project is to study the characters and matrix coefficients of the representations of the classical groups from the view point of the theory of reductive dual pairs. In particular of interest are formulas for the characters in terms of the natural moment maps, and the wave front sets. Regarding the matrix coefficients, the central question is to decide which absolutely integrable positive definite matrix coefficients have positive integral, and corollaries regarding the preservation of unitarity under Howe's correspondence.We shall apply the ideas sketched above to signal processing. Specifically we are interested in the information compression and denoising of signals which are well balanced in the time-frequency domain.