Idempotents with polynomial coefficients

TL;DR

This paper introduces a method to construct idempotents with polynomial coefficients by combining Young idempotents and the symmetric group's action on Vandermonde determinants, advancing algebraic combinatorics.

Contribution

It presents a novel approach to generate polynomial coefficient idempotents using Young idempotents and symmetric group actions on Vandermonde determinants.

Findings

Constructed new idempotents with polynomial coefficients.

Linked Young idempotents with Vandermonde determinant actions.

Enhanced understanding of algebraic structures in symmetric groups.

Abstract

We combine Young idempotents in the group algebra of the symmetric group with the action of the symmetric group on products of Vandermonde determinants to obtain idempotents with polynomial coefficients.