Geometry of infinite dimensional unitary groups: convexity and fixed points

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 ...

a note on fixed points of automorphisms of infinite groups

‎motivated by a celebrated theorem of schur‎, ‎we show that if~$gamma$ is a normal subgroup of the full automorphism group $aut(g)$ of a group $g$ such that $inn(g)$ is contained in $gamma$ and $aut(g)/gamma$ has no uncountable abelian subgroups of prime exponent‎, ‎then $[g,gamma]$ is finite‎, ‎provided that the subgroup consisting of all elements of $g$ fixed by $gamma$ has finite index‎. ‎so...

The Geometry of Infinite-Dimensional Groups

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...

Heat kernel measures and Riemannian geometry on infinite-dimensional groups

I will describe a construction of heat kernel measures on GL(H), the group of invertible operators on a complex Hilbert space H. This measure is determined by an infinite dimensional Lie algebra g and a Hermitian inner product on it. The main tool in this construction is a diffusion in a Hilbert space ambient g. Then I’ll describe holomorphic functions and their properties. One of interesting n...