This volume records most of the talks given at the Conference on Infinite-dimensional Groups held at the Mathematical Sciences Research Institute at Berkeley, California, May 10-May 15, 1984, as a part of the special program on Kac-Moody Lie algebras. The purpose of the conference was to review recent developments of the theory of infinite-dimensional groups and its applications. The present collection concentrates on three very active, interrelated directions of the field: general Kac-Moody groups, gauge groups (especially loop groups) and diffeomorphism groups. I would like to express my thanks to the MSRI for sponsoring the meeting, to Ms. Faye Yeager for excellent typing, to the authors for their manuscripts, and to Springer-Verlag for publishing this volume. V. Kac INFINITE DIMENSIONAL GROUPS WITH APPLICATIONS CONTENTS The Lie Group Structure of M. Adams. T. Ratiu 1 Diffeomorphism Groups and & R. Schmid Invertible Fourier Integral Operators with Applications On Landau-Lifshitz Equation and E. Date 71 Infinite Dimensional Groups Flat Manifolds and Infinite D. S. Freed 83 Dimensional Kahler Geometry Positive-Energy Representations R. Goodman 125 of the Group of Diffeomorphisms of the Circle Instantons and Harmonic Maps M. A. Guest 137 A Coxeter Group Approach to Z. Haddad 157 Schubert Varieties Constructing Groups Associated to V. G. Kac 167 Infinite-Dimensional Lie Algebras I. Kaplansky 217 Harish-Chandra Modules Over the Virasoro Algebra & L. J. Santharoubane 233 Rational Homotopy Theory of Flag S.

Inhalt
The Lie Group Structure of Diffeomorphism Groups and Invertible Fourier Integral Operators with Applications.- On Landau-Lifshitz Equation and Infinite Dimensional Groups.- Flat Manifolds and Infinite Dimensional Kähler Geometry.- Positive-Energy Representations of the Group of Diffeomorphisms of the Circle.- Instantons and Harmonic Maps.- A Coxeter Group Approach to Schubert Varieties.- Constructing Groups Associated to Infinite-Dimensional Lie Algebras.- Harish-Chandra Modules Over the Virasoro Algebra.- Rational Homotopy Theory of Flag Varieties Associated to Kac-Moody Groups.- The Two-Sided Cells of the Affine Weyl Group of Type Ãn.- Loop Groups, Grassmannians and KdV Equations.- An Adjoint Quotient for Certain Groups Attached to Kac-Moody Algebras.- Analytic and Algebraic Aspects of the Kadomtsev-Petviashvili Hierarchy from the Viewpoint of the Universal Grassmann Manifold.- Comments on Differential Invariants.- The Virasoro Algebra and the KP Hierarchy.