The dual Specht module of the symmetric group algebra over $\mathbb{Q}$ has two distinguished bases, namely the standard basis and Young’s seminormal basis. We study how the Young’s seminormal basis vectors are expressed in terms of the standard basis, as well as the denominators of the coefficients in these expressions. We obtain closed formula for some Young’s seminormal basis vectors, as well as partial results for the denominators in general.
This is a joint work with Ming Fang (Chinese Academy of Sciences) and Kay Jin Lim (Nanyang Technological University).