Title | Infinite Dimensional Groups with Applications [electronic resource] / edited by V. Kac |
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Imprint | New York, NY : Springer New York : Imprint: Springer, 1985 |

Connect to | http://dx.doi.org/10.1007/978-1-4612-1104-4 |

Descript | X, 380 p. online resource |

SUMMARY

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

CONTENT

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 Kรคhler 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 ร{131}n -- 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

Mathematics
Group theory
Mathematics
Group Theory and Generalizations