Abstract
We realize the integral Specht modules for the symmetric group S n as induced modules from the subalgebra of the group algebra generated by the Jucys–Murphy elements. We deduce from this that the simple modules for \({{\mathbb F}_p} S_n \) are generated by reductions modulo p of the corresponding Jucys–Murphy idempotents.
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Supported in part by Programa Reticulados y Simetría, by the FONDECYT grants 1090701 and 1121121 and by the MathAmSud project OPECSHA 01-math-10.
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Ryom-Hansen, S. Young’s Seminormal Form and Simple Modules for S n in Characteristic p . Algebr Represent Theor 16, 1587–1609 (2013). https://doi.org/10.1007/s10468-012-9372-0
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DOI: https://doi.org/10.1007/s10468-012-9372-0