Harmonic analysis on Lie groups via hypergroup convolution structures

点击翻译按钮获取中文摘要

Harmonic analysis on Lie groups via hypergroup convolution structures. This project studies convolution structures for conjugacy classes\r\nof nilpotent and compact Lie groups and the connections with fusion rule algebras. The aims are to establish a suitable theory of almost periodic functions on a nilpotent Lie group to allow a\r\nwrapping theorem to be formulated, to describe precisely the\r\nclass hypergroup of a compact Lie group, and to clarify the relations of the latter with fusion rule algebras. This will result in further understanding of the Kirillov orbit method and the have applications to conformal field theory.