For a partition of , let be the ideal of generated by all Specht polynomials of shape . We show that if is Cohen–Macaulay then is of the form either , , or . We also prove that the converse is true in the case. To show the latter statement, the radicalness of these ideals and a result of Etingof et al. are crucial. We also remark that is not Cohen–Macaulay if and only if .
"When is a Specht ideal Cohen–Macaulay?." J. Commut. Algebra 13 (4) 589 - 608, Winter 2021. https://doi.org/10.1216/jca.2021.13.589