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April 2003 Elliptic Hecke algebras and modified Cherednik algebras
Tadayoshi Takebayashi
Proc. Japan Acad. Ser. A Math. Sci. 79(4): 80-84 (April 2003). DOI: 10.3792/pjaa.79.80

Abstract

The elliptic Hecke algebras associated to the 1-codimensional elliptic root systems have been defined by H. Yamada [10], which are subalgebras of Cherednik's double affine Hecke algebras [2, 3]. The elliptic Hecke algebras associated to the elliptic root systems of type $X^{(1,1)}$ have been defined similarly by the author [11] in terms of generators and relations associated to the completed elliptic diagram. On the other hand, M. Kapranov [6] has defined modified Cherednik algebras associated to the double coset decomposition of the group schemes over 2-dimensional local field. In this paper, we see that modified Cherednik algebras are isomorphic to elliptic Hecke algebras of type $X^{(1,1)}$.

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Tadayoshi Takebayashi. "Elliptic Hecke algebras and modified Cherednik algebras." Proc. Japan Acad. Ser. A Math. Sci. 79 (4) 80 - 84, April 2003. https://doi.org/10.3792/pjaa.79.80

Information

Published: April 2003
First available in Project Euclid: 18 May 2005

zbMATH: 1045.22019
MathSciNet: MR1976361
Digital Object Identifier: 10.3792/pjaa.79.80

Subjects:
Primary: 22E50

Keywords: double affine Hecke algebras , elliptic Hecke algebras , modified Cherednik algebras

Rights: Copyright © 2003 The Japan Academy

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Vol.79 • No. 4 • April 2003
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