Algebraic and Analytic Methods in Representation Theory

Representational theory for reductive groups is central to much of mathematics and mathematical analysis. The methods employed are algebraic as well as analytic in nature, and the subject requires a broad knowledge. In this book, introductions are given to five perspectives in reduction groups: modular representations of algebraic groups and relations to quantum groups; orbital varieties, goldie rank polynomials and unitary highest weight modules; discontinuous groups and Clifford-Klein forms of pseudo-Riemannian homogenous manifolds; the method of stationary phase and applications to geometry and analysis on Lie groups; and the orbit method and unitary representations for reductive Lie groups.