Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The $r$-matrix structure of Hitchin systems via loop group uniformization

Raschid Abedin

Abstract

In this work, the description of the moduli space of principal $G$-bundles as double quotient of loop groups is used to construct an étale local $r$-matrix for the Hitchin integrable system.

The $r$-matrix structure of Hitchin systems via loop group uniformization

Abstract

In this work, the description of the moduli space of principal -bundles as double quotient of loop groups is used to construct an étale local -matrix for the Hitchin integrable system.
Paper Structure (57 sections, 133 equations)

This paper contains 57 sections, 133 equations.

Table of Contents

  1. Introduction
  2. Loop groups, the moduli space of $G$-bundles, and the Hitchin system
  3. The loop groups
  4. The complete loop group
  5. The inner loop group
  6. Coordinate representation
  7. The outer loop group
  8. The loop algebras
  9. Geometric structure of loop algebras
  10. Vector fields on $LG$
  11. Poisson structure of $T^*LG$
  12. Moduli spaces of $G$-bundles
  13. The complete loop group $LG$ as moduli space
  14. The flag varieties as moduli space
  15. The moduli space of $G$-bundles and loop group uniformization
  16. ...and 42 more sections