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Affine Flag Manifolds and Principal Bundles

  • Conference proceedings
  • © 2010

Overview

Editors:
  1. Alexander Schmitt

    1. Institut für Mathematik, Freie Universität Berlin, Berlin, Germany

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  • User-friendly introductions to interesting fields of active current research
  • Contributions written by internationally renowned experts
  • No textbooks available on these topics so far
  • Includes supplementary material: sn.pub/extras

Part of the book series: Trends in Mathematics (TM)

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Table of contents (9 papers)

  1. Front Matter

    Pages i-xii
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  2. Affine Springer Fibers and Affine Deligne-Lusztig Varieties

    • Ulrich Görtz
    Pages 1-50

  3. Quantization of Hitchin’s Integrable System and the Geometric Langlands Conjecture

    • Tomás L. Gómez
    Pages 51-90

  4. Faltings’ Construction of the Moduli Space of Vector Bundles on a Smooth Projective Curve

    • Georg Hein
    Pages 91-122

  5. Lectures on the Moduli Stack of Vector Bundles on a Curve

    • Jochen Heinloth
    Pages 123-153

  6. On Moduli Stacks of G-bundles over a Curve

    • Norbert Hoffmann
    Pages 155-163

  7. Clifford Indices for Vector Bundles on Curves

    • Herbert Lange, Peter E. Newstead
    Pages 165-202

  8. Division Algebras and Unit Groups on Surfaces

    • Fabian Reede, Ulrich Stuhler
    Pages 203-217

  9. A Physics Perspective on Geometric Langlands Duality

    • Karl-Georg Schlesinger
    Pages 219-232

  10. Double Affine Hecke Algebras and Affine Flag Manifolds, I

    • Michela Varagnolo, Eric Vasserot
    Pages 233-289
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Keywords

About this book

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.

Editors and Affiliations

  • Institut für Mathematik, Freie Universität Berlin, Berlin, Germany

    Alexander Schmitt

Bibliographic Information

  • Book Title: Affine Flag Manifolds and Principal Bundles

  • Editors: Alexander Schmitt

  • Series Title: Trends in Mathematics

  • DOI: https://doi.org/10.1007/978-3-0346-0288-4

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Birkhäuser Basel 2010

  • Hardcover ISBN: 978-3-0346-0287-7Published: 22 June 2010

  • Softcover ISBN: 978-3-0348-0309-0Published: 05 September 2012

  • eBook ISBN: 978-3-0346-0288-4Published: 28 January 2011

  • Series ISSN: 2297-0215

  • Series E-ISSN: 2297-024X

  • Edition Number: 1

  • Number of Pages: 290

  • Topics: Algebraic Geometry

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