Doug Pickrell

Measures on infinite dimensional Grassmann manifolds

Abstract A 1-parameter family of quasi-invariant measures is presented. These measures are cylinder measures in graph coordinates. Their characteristic functions are represented as integrals relative to an infinite product measure. This is applied to the problem of determining the support properties of the measures. One of the measures can be used to define the unitary structure for the basic representation of the affine extension of the restricted unitary group.

Separable representations for automorphism groups of infinite symmetric spaces

Abstract In this paper we consider the separable unitary representations for the automorphism groups of the classical infinite rank (Finsler) symmetric spaces defined by Schatten p -classes (often referred to as restricted groups). Following earlier work of Olshanskii and Voiculescu, it is shown that the spherical representations are always type I, the form of the irreducible spherical functions is determined, and their analyticity established. Using an intuitive geometric argument, it is shown that the real spherical functions extend to the Hilbert-Schmidt limit and never beyond. This yields a complete determination of the separable representations for groups corresponding to p -classes with p > 2.

On the Mickelsson-Faddeev extension and unitary representations

The Mickelsson-Faddeev extension is a 3-space analogue of a Kac-Moody group, where the central charge is replaced by a space of functions of the gauge potential. This extension is a pullback of a universal extension, where the gauge potentials are replaced by operators in a Schatten ideal, as in non-commutative differential geometry. Our main result is that the universal extension cannot be faithfully represented by unitary operators on a separable Hilbert space. We also examine potential consequences of the existence of unitary representations for the Mickelsson-Faddeev extension.

Invariant measures for unitary groups associated to Kac-Moody Lie algebras

General introduction Part I. General Theory: The formal completions of

Homogeneous Poisson Structures on Loop Spaces of Symmetric Spaces

G(A)

The orbit method and the Virasoro extension of Diff+(S1): I. Orbital integrals

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P(ϕ)2 Quantum Field Theories and Segal’s Axioms

G(A)/B

On Y M2 measures and area-preserving diffeomorphisms

Measures on the formal flag space Part II. Infinite Classical Groups: Introduction for Part II Measures on the formal flag space The case

Loops in SU(2), Riemann Surfaces, and Factorization, I ?

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On the support of quasi-invariant measures on infinite-dimensional Grassmann manifolds

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