Mathematical Sciences: Group Theory and Differential Geometry

点击翻译按钮获取中文摘要

9625941 Kostant This project deals with research in various topics related to representations and geometric quantization of classical as well as exceptional Lie groups. The investigator proposes to find new approaches to representing the character of an irreducible representation as the Fourier transform of a coadjoint orbit. Singular representations, the quantum cohomology ring of the flag manifold, and representations of a semisimple Lie algebra appearing in its exterior algebra are among the topics to be pursued. Lie groups often arise as symmetry groups. For example, so called unitary Lie groups describe symmetries in elementary particles. Another example is provided by the Carbon 60 molecule, popularly known as the buckyball. Here the full symmetry group turns out to be an exceptional Lie group. There are only finitely many exceptional groups - whereas the number of classical groups are infinite - and much work has been done on how to realize them as subgroups of classical groups.