On the denominators of Young's seminormal basis

DOI10.1016/J.JCTA.2022.105645arXiv0904.4243WikidataQ114162639 ScholiaQ114162639MaRDI QIDQ6213702

Publication date: 27 April 2009

Abstract: We study the seminormal basis

f_{t}

for the Specht modules of the Iwahori-Hecke algebra

{c a l 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.

Mathematics Subject Classification ID

Lie algebras and Lie superalgebras (17Bxx) Representation theory of groups (20Cxx) Algebraic combinatorics (05Exx)

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