On representations of cyclotomic Hecke algebras

TL;DR

This paper develops a new approach to the representation theory of cyclotomic Hecke algebras using Jucys--Murphy elements, establishing their maximality and proposing a basis that demonstrates deformation flatness.

Contribution

It introduces a basis for cyclotomic Hecke algebras and proves the maximality of Jucys--Murphy elements, providing a novel perspective on their structure and deformation.

Findings

Maximality of Jucys--Murphy elements established

A new basis for cyclotomic Hecke algebras proposed

Flatness of deformation demonstrated without representation theory

Abstract

An approach, based on Jucys--Murphy elements, to the representation theory of cyclotomic Hecke algebras is developed. The maximality (in the cyclotomic Hecke algebra) of the set of the Jucys--Murphy elements is established. A basis of the cyclotomic Hecke algebra is suggested; this basis is used to establish the flatness of the deformation without use of the representation theory.