Matrix units and Schur elements for the degenerate cyclotomic Hecke algebras

TL;DR

This paper provides explicit descriptions of matrix units, Schur elements, and orthogonal bases for Specht modules in the context of degenerate cyclotomic Hecke algebras, advancing the algebraic understanding of their structure.

Contribution

It introduces explicit formulas for Schur elements and orthogonal bases using cellular basis techniques, enhancing the structural analysis of degenerate cyclotomic Hecke algebras.

Findings

Explicit formulas for Schur elements derived

Orthogonal bases for Specht modules constructed

Closed-form bilinear form on Specht modules obtained

Abstract

The paper uses the cellular basis of the (semi-simple) degenerate cyclotomic Hecke algebras to investigate these algebras exhaustively. As a consequence, we describe explicitly the "Young's seminormal form" and a orthogonal bases for Specht modules and determine explicitly the closed formula for the natural bilinear form on Specht modules and Schur elements for the degenerate cyclotomic Hekce algebras.