On the denominators of Young's seminormal basis

Abstract

We study the seminormal basis ${f_t}$ for the Specht modules of the Iwahori-Hecke algebra ${\cal H}_n(q)$ of type $A_{n-1}$. We focus on the base change coefficients between the seminormal basis ${f_t}$ and Young's natural basis ${x_t}$ with emphasis on the denominators of these coefficients. In certain important cases we obtain simple formulas for these coefficients involving radial lengths. Even for general tableaux we obtain new formulas. On the way we prove a new result about summands of the restricted Specht module at root of unity.