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LSpice
LSpice
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I believe this question is answered (at least for the case of the symmetric group) by the "higher Specht basis" of Ariki, Terasoma, and Yamada; see the recent preprint https://arxiv.org/abs/2005.02110Gillespie and Rhoades - Higher Specht bases for generalizations of the coinvariant ring for a discussion of this problem in a broader context.

I believe this question is answered (at least for the case of the symmetric group) by the "higher Specht basis" of Ariki, Terasoma, and Yamada; see the recent preprint https://arxiv.org/abs/2005.02110 for a discussion of this problem in a broader context.

I believe this question is answered (at least for the case of the symmetric group) by the "higher Specht basis" of Ariki, Terasoma, and Yamada; see the recent preprint Gillespie and Rhoades - Higher Specht bases for generalizations of the coinvariant ring for a discussion of this problem in a broader context.

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Sam Hopkins
Sam Hopkins
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I believe this question is answered (at least for the case of the symmetric group) by the "higher Specht basis" of Ariki, Terasoma, and Yamada; see the recent preprint https://arxiv.org/abs/2005.02110 for a discussion of this problem in a broader context.