By Lajos Pukanszky
This publication provides to the nice physique of study that extends again to A. Weil and E. P. Wigner at the unitary representations of in the neighborhood compact teams and their characters, i.e. the interaction among classical workforce thought and glossy research. The teams studied listed here are the attached Lie teams of normal kind (not unavoidably nilpotent or semisimple).
Final effects replicate Kirillov's orbit strategy; relating to teams which may be non-algebraic or non-type I, the strategy calls for substantial sophistication. tools used diversity from deep useful research (the concept of C∗-algebras, components from F. J. Murray and J. von Neumann, and degree conception) to differential geometry (Lie teams and Hamiltonian actions).
This booklet provides for the 1st time a scientific and concise compilation of proofs formerly dispersed in the course of the literature. the result's a magnificent instance of the deepness of Pukánszky's work.
Readership: Graduate scholars and examine mathematicians operating in topological teams and Lie teams; theoretical physicists