Generalized Markov traces and Jucys-Murphy elements

TL;DR

This paper introduces a new, simplified method for constructing Markov traces on Iwahori-Hecke algebras across various Coxeter groups, extending known techniques especially in types B and D.

Contribution

It provides a novel, unified construction of Markov traces for infinite series of Coxeter groups, including new results in types B and D, generalizing previous type A methods.

Findings

New construction of Markov traces for types B and D

Generalization of type A symmetric polynomial approach

Extension of trace theory to broader Coxeter groups

Abstract

We give a simple construction of Markov traces for Iwahori-Hecke algebras associated with infinite series of crystallographic Coxeter groups. In types B and D it is new, and generalizes a known construction in type A employing symmetric polynomials in multiplicative Jucys-Murphy elements.