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On Hecke Algebras Associated with Elliptic Root Systems

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Representation Theory of Algebraic Groups and Quantum Groups

Part of the book series: Progress in Mathematics ((PM,volume 284))

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Abstract

We define the elliptic Hecke algebras for arbitrary marked elliptic root systems in terms of the corresponding elliptic Dynkin diagrams and make a “dictionary” between the elliptic Hecke algebras and the double affine Hecke algebras.

Mathematics Subject Classifications (2000): Primary 17B35; Secondary 14D30, 16G20

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Author information

Authors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, 153-8914, Japan

    Yoshihisa Saito

Authors
  1. Yoshihisa Saito
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  2. Midori Shiota
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Corresponding author

Correspondence to Yoshihisa Saito .

Editor information

Editors and Affiliations

  1. Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan

    Akihiko Gyoja

  2. Research Institute for Mathematical Scie, Kyoto University, Kyoto, 606-8502, Japan

    Hiraku Nakajima

  3. Faculty of Science and Technology, Sophia University, Department of Information and Communication Sciences -1, Tokyo, 102-8554, Japan

    Ken-ichi Shinoda

  4. Graduate School of Mathematics, Nagoya University, Nagoya, 464-8602, Japan

    Toshiaki Shoji

  5. Graduate School of Science, Osaka City University, Department of Mathematics -3-138, Osaka, 558-8585, Japan

    Toshiyuki Tanisaki

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Saito, Y., Shiota, M. (2010). On Hecke Algebras Associated with Elliptic Root Systems. In: Gyoja, A., Nakajima, H., Shinoda, Ki., Shoji, T., Tanisaki, T. (eds) Representation Theory of Algebraic Groups and Quantum Groups. Progress in Mathematics, vol 284. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4697-4_12

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