Infinite Dimensional Groups with Applications

1. Front Matter

   Pages i-x

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2. The Lie Group Structure of Diffeomorphism Groups and Invertible Fourier Integral Operators with Applications

   • Malcolm Adams, Tudor Ratiu, Rudolf Schmid

   Pages 1-69

3. On Landau-Lifshitz Equation and Infinite Dimensional Groups

   • Etsuro Date, Michio Jimbo, Masaki Kashiwara, Tetsuji Miwa

   Pages 71-81

4. Flag Manifolds and Infinite Dimensional Kähler Geometry

   • D. S. Freed

   Pages 83-124

5. Positive-Energy Representations of the Group of Diffeomorphisms of the Circle

   • Roe Goodman, Nolan R. Wallach

   Pages 125-135

6. Instantons and Harmonic Maps

   • M. A. Guest

   Pages 137-156

7. A Coxeter Group Approach to Schubert Varieties

   • Ziad Haddad

   Pages 157-165

8. Constructing Groups Associated to Infinite-Dimensional Lie Algebras

   • Victor G. Kac

   Pages 167-216

9. Harish-Chandra Modules Over the Virasoro Algebra

   • Irving Kaplansky, L. J. Santharoubane

   Pages 217-231

10. Rational Homotopy Theory of Flag Varieties Associated to Kac-Moody Groups

    • Shrawan Kumar

    Pages 233-273

11. The Two-Sided Cells of the Affine Weyl Group of Type Ãn

    • George Lusztig

    Pages 275-283

12. Loop Groups, Grassmannians and KdV Equations

    • Andrew Pressley

    Pages 285-306

13. An Adjoint Quotient for Certain Groups Attached to Kac-Moody Algebras

    • Peter Slodowy

    Pages 307-333

14. Analytic and Algebraic Aspects of the Kadomtsev-Petviashvili Hierarchy from the Viewpoint of the Universal Grassmann Manifold

    • Kimio Ueno

    Pages 335-353

15. Comments on Differential Invariants

    • B. Weisfeiler

    Pages 355-370

16. The Virasoro Algebra and the KP Hierarchy

    • Hirofumi Yamada

    Pages 371-380

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.

• Applications
• Division
• Groups
• Invariant
• Lie
• Mathematica
• Volume
• algebra
• development
• diffeomorphism
• geometry
• homotopy theory
• integral
• lie group
• presentation

• Department of Mathematics, Massachusetts Institute of Technology, Cambridge, USA

  V. Kac

• Mathematical Sciences Research Institute, Berkeley, USA

  V. Kac

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