Unitary structure in representations of infinite-dimensional groups and a convexity theorem

Unitary structure in representations of infinite-dimensional groups and a convexity theorem

In this paper, we show that a K a c M o o d y algebra fl(A) associated to a symmetr izable generalized Car tan matr ix A carries a cont ravar ian t Hermi t i an form which is positive-definite on all root spaces. We deduce that every integrable highest weight g(A)-module L(A) carries a cont ravar ian t positivedefinite Hermi t i an form. This allows us to define the m o m e n t m a p and prove ...

Infinite-dimensional Representations of Real Reductive Groups

is continuous. “Locally convex” means that the space has lots of continuous linear functionals, which is technically fundamental. “Complete” allows us to take limits in V , and so define things like integrals and derivatives. The representation (π, V ) is irreducible if V has exactly two closed invariant subspaces (which are necessarily 0 and V ). The representation (π, V ) is unitary if V is a...

Infinite Dimensional Groups, Their Representations, Orbits, Invariants

1. Representation theory for infinite dimensional groups does not exist as a theory although such groups occur long ago in several branches of mathematics and its applications. Among the most important examples are: (a) groups of automorphisms of infinite dimensional vector spaces with some additional structures (unitary, symplectic, Fredholm etc.); (b) groups of diffeomorpliisms of smooth mani...

0 Wavelet filters and infinite - dimensional unitary groups

Abstract. In this paper, we study wavelet filters and their dependence on two numbers, the scale N and the genus g. We show that the wavelet filters, in the quadrature mirror case, have a harmonic analysis which is based on representations of the C∗-algebra ON . A main tool in our analysis is the infinite-dimensional group of all maps T → U (N) (where U (N) is the group of all unitary N-by-N ma...

Irreducible Representations of Infinite-dimensional Transformation Groups and Lie Algebras