Alexander Schmitt 
Affine Flag Manifolds and Principal Bundles 

Affine flag manifolds are infinite dimensional versions of familiar objects such as Graßmann varieties. The book features lecture notes, survey articles, and research notes – based on workshops held in Berlin, Essen, and Madrid – explaining the significance of these and related objects (such as double affine Hecke algebras and affine Springer fibers) in representation theory (e.g., the theory of symmetric polynomials), arithmetic geometry (e.g., the fundamental lemma in the Langlands program), and algebraic geometry (e.g., affine flag manifolds as parameter spaces for principal bundles). Novel aspects of the theory of principal bundles on algebraic varieties are also studied in the book.

Table of Content

Affine Springer Fibers and Affine Deligne-Lusztig Varieties.- Quantization of Hitchin’s Integrable System and the Geometric Langlands Conjecture.- Faltings’ Construction of the Moduli Space of Vector Bundles on a Smooth Projective Curve.- Lectures on the Moduli Stack of Vector Bundles on a Curve.- On Moduli Stacks of G-bundles over a Curve.- Clifford Indices for Vector Bundles on Curves.- Division Algebras and Unit Groups on Surfaces.- A Physics Perspective on Geometric Langlands Duality.- Double Affine Hecke Algebras and Affine Flag Manifolds, I.