Jucys-Murphy elements and centers of cellular algebras

TL;DR

This paper investigates the conditions under which the center of a cellular algebra's extension over its field of fractions is generated by symmetric polynomials in Jucys-Murphy elements, providing a clear criterion.

Contribution

It establishes a necessary and sufficient condition for the center of the extended algebra to be generated by symmetric polynomials in Jucys-Murphy elements.

Findings

Center of $A_K$ is generated by symmetric polynomials in Jucys-Murphy elements under the given condition.

Provides a criterion linking Jucys-Murphy elements to the algebra's center.

Enhances understanding of the structure of cellular algebras and their centers.

Abstract

Let R be an integral domain and A a cellular algebra. Suppose that A is equipped with a family of Jucys-Murphy elements which satisfy the separation condition. Let K be the field of fractions of R. We give a necessary and sufficient condition under which the center of $A_{K}$ consists of the symmetric polynomials in Jucys-Murphy elements.