In J , Jones used the Markov traces on the Hecke algebras of type A to construct the knot invariants. Motivated by Jones's work, Lambropoulou w x L introduced the Markov traces on the cyclotomic Hecke algebras of type Ε½ . Ε½ w x . G m, 1, r see GL for the case m s 2 . Since any linear trace function can be expressed as a linear combination of the irreducible characters, where the coefficients are called weights, it is natural to ask how to determine the weights of the Markov traces.
w x In W1 , Wenzl proved that the weights of the Markov traces on the Ε½ . Hecke algebras of type A i.e., m s 1 can be expressed via Schur Ε½ Ε½ .. w x functions see 3.3 . In O , Orellana proved that there is an epimorphism Ε½ . from the Hecke algebra of type B i.e., m s 2 with special parameters to some reduced algebra of a type-A Hecke algebra. This enabled her to use Wenzl's result to determine the weights of the Markov traces on type-B w x Hecke algebras. In I , Iancu gave a conjecture about the general weight formulas of the type-B Hecke algebras.
The main purpose of this paper is to determine the weights of the Ε½ . Markov traces on the cyclotomic Hecke algebras of type G m, 1, r , w x w generalizing the results in O . Our arguments are based on those in loc.
x cit . However, we will not use the results on Jones basic construction.
The content of this paper is organized as follows. In Section 1, we collect some of the results on type-A Hecke algebras. We discuss the cyclotomic Hecke algebras in Section 2. The main result of this section is the