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

Mee Seong Im

doi:10.1216/rmj.2021.51.1671

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 the parabolic Hecke algebra.

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Mee Seong Im. "A short proof on the transition matrix from the Specht basis to the Kazhdan–Lusztig basis." Rocky Mountain J. Math. 51 (5) 1671 - 1680, October 2021. https://doi.org/10.1216/rmj.2021.51.1671

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Received: 9 December 2019; Revised: 9 February 2021; Accepted: 6 March 2021; Published: October 2021

First available in Project Euclid: 17 February 2022

MathSciNet: MR4382990

zbMATH: 1487.05273

Digital Object Identifier: 10.1216/rmj.2021.51.1671

Subjects:

Primary: 05E10

Secondary: 20C08 , 20C30

Keywords: Kazhdan–Lusztig basis , parabolic Hecke algebra , Specht module

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