The Lusztig isomorphism for Hecke algebras of dihedral type (Q912971)

Let W denote a finite Coxeter group and H the Hecke algebra of W over \({\mathbb{Q}}(q^{1/2})\), where q is an indeterminate. For W satisfying a certain condition, which holds for Weyl groups, \textit{G. Lusztig} [J. Algebra 71, 490-498 (1981; Zbl 0465.20042)] gave an isomorphism of H to the group algebra of W over \({\mathbb{Q}}(q^{1/2}).\) The author gives explicit formulas for this isomorphism in the case of W being of dihedral type. The author determines the images of the generators of H and of a certain basis of the center of the Hecke algebra H.