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Theta Functions Associated with Affine Root Systems and the Elliptic Ruijsenaars Operators

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Physical Combinatorics

Part of the book series: Progress in Mathematics ((PM,volume 191))

Abstract

We study a family of mutually commutative difference operators associated with affine root systems. These operators act on the space of meromorphic functions on the Cartan subalgebra of the affine Lie algebra. We show that the space spanned by characters of a fixed positive level is invariant under the action of these operators.

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Author information

Authors and Affiliations

  1. Graduate School of Science, University of Tokyo, Hongo 7-3-1 Bunkyo, Bunkyo, Tokyo 113, Japan

    Yasushi Komori

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  1. Yasushi Komori
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Editor information

Editors and Affiliations

  1. Research Institute for Mathematical Sciences (RIMS), Kyoto University, 606-01, Kyoto, Japan

    Masaki Kashiwara  & Tetsuji Miwa  & 

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Komori, Y. (2000). Theta Functions Associated with Affine Root Systems and the Elliptic Ruijsenaars Operators. In: Kashiwara, M., Miwa, T. (eds) Physical Combinatorics. Progress in Mathematics, vol 191. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1378-9_4

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  • DOI: https://doi.org/10.1007/978-1-4612-1378-9_4

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7121-5

  • Online ISBN: 978-1-4612-1378-9

  • eBook Packages: Springer Book Archive

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