On the denominators of Young's seminormal basis

Details On the denominators of Young's seminormal basis On the denominators of Young's seminormal basis

2009-04-27

arxiv.org/abs/0904.4243v3

Mathematics

Representation Theory

21 pages. The paper has been completely rewritten. The basic setting is now that of Iwahori-Hecke algebras of type $A$

Scientific paper

We study the seminormal basis ${f\_t}$ for the Specht modules of the Iwahori-Hecke algebra $\cal H\_{q,n}$ of type $A_{n-1}$. We focus on the base change coefficients between the seminormal basis ${f\_t}$ and Young's natural basis ${e\_t}$ 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.

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