Elliptic Hecke algebras and modified Cherednik algebras

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