$q$-deformation of the group algebra $k[\widehat {W}]$ associated to the elliptic root system $A_l^{(1,1)}$ ($l \geq 2$)

Abstract

In the case of elliptic root system $A_l^{(1,1)}$ ($l \geq 2$), a $q$-deformation algebra of the hyperbolic extension of the elliptic Weyl group is constructed by using a representation according to Kazhdan-Lusztig.