Generalised Markov traces and Jucys–Murphy elements

We give a simple construction of Markov traces for Iwahori–Hecke algebras associated with the crystallographic Coxeter groups of types upper A Subscript n Baseline comma upper B Subscript n Baseline A n , B n Aₙ, Bₙ and upper D Subscript n D n Dₙ . In types upper B B B and upper D D D , it is new and generalises a known construction in type upper A A A employing symmetric polynomials in multiplicative Jucys–Murphy elements.