The r-Matrix Structure of Hitchin Systems via Loop Group Uniformization

Abstract In this work, the description of the moduli space of principal $$G$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>G</mml:mi> </mml:math> -bundles as double quotient of loop groups is used to construct an étale local $$r$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>r</mml:mi> </mml:math> -matrix for the Hitchin integrable system.