Proceedings of the Japan Academy, Series A, Mathematical Sciences

Elliptic Hecke algebras and modified Cherednik algebras

Tadayoshi Takebayashi

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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 $X^{(1,1)}$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 79, Number 4 (2003), 80-84.

Dates
First available in Project Euclid: 18 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1116443658

Digital Object Identifier
doi:10.3792/pjaa.79.80

Mathematical Reviews number (MathSciNet)
MR1976361

Zentralblatt MATH identifier
1045.22019

Subjects
Primary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]

Keywords
Double affine Hecke algebras elliptic Hecke algebras modified Cherednik algebras

Citation

Takebayashi, Tadayoshi. Elliptic Hecke algebras and modified Cherednik algebras. Proc. Japan Acad. Ser. A Math. Sci. 79 (2003), no. 4, 80--84. doi:10.3792/pjaa.79.80. https://projecteuclid.org/euclid.pja/1116443658


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