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.
Cite this article
Yoshihisa Saito, Midori Shiota, On Hecke Algebras Associated with Elliptic Root Systems and the Double Affine Hecke Algebras. Publ. Res. Inst. Math. Sci. 45 (2009), no. 3, pp. 845–905