On the idempotents of Hecke algebras

TL;DR

This paper introduces a novel construction method for primitive idempotents in Hecke algebras linked to symmetric groups, utilizing evaluated products of rational functions, and relates normalization factors to the Ocneanu--Markov trace.

Contribution

It presents a new fusion procedure for Hecke algebras, providing explicit evaluated product formulas for primitive idempotents and connecting normalization factors to the Ocneanu--Markov trace.

Findings

Explicit formulas for primitive idempotents in Hecke algebras

Connection between normalization factors and Ocneanu--Markov trace

A new fusion procedure for constructing idempotents

Abstract

We give a new construction of primitive idempotents of the Hecke algebras associated with the symmetric groups. The idempotents are found as evaluated products of certain rational functions thus providing a new version of the fusion procedure for the Hecke algebras. We show that the normalization factors which occur in the procedure are related to the Ocneanu--Markov trace of the idempotents.