Functional determinants and representation theory

Functional determinants provide a way, using zeta
functions, of defining the determinants of certain elliptic
differential operators on compact manifolds. In this lecture
we shall study how such determinants depend on the geometric
data and explain how this is connected to representation theory
of semisimple Lie groups. Functional determinants play a role
in string theory and other physical theories, and the
representation theory involves inequalities satisfied by
Knapp-Stein intertwining operators.