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

摘要本课题的目的是从约化对偶理论的角度研究经典群表示的特征和矩阵系数。我们特别感兴趣的是用自然矩映射和波前集表示特征的公式。对于矩阵系数，中心问题是确定哪些绝对可积的正定矩阵系数具有正积分，以及关于在Howe对应下保持一致性的推论。我们将把上面概述的思想应用于信号处理。具体来说，我们感兴趣的是信号的信息压缩和去噪，这些信号在时频域中很好地平衡。

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.