A short proof on the transition matrix from the Specht basis to the Kazhdan-Lusztig basis

TL;DR

This paper presents a concise proof for the coefficients that convert the Specht basis to the Kazhdan-Lusztig basis, utilizing Kazhdan-Lusztig theory for parabolic Hecke algebras.

Contribution

It offers a simplified proof of the basis transition coefficients leveraging Kazhdan-Lusztig theory, enhancing understanding of basis transformations in representation theory.

Findings

Short proof of basis transition coefficients

Utilizes Kazhdan-Lusztig theory for parabolic Hecke algebra

Simplifies previous approaches to basis change

Abstract

We provide a short proof on the change-of-basis coefficients from the Specht basis to the Kazhdan-Lusztig basis, using Kazhdan-Lusztig theory for parabolic Hecke algebra.