## Abstract

Given a partition λ of n, consider the subspace E_{λ} of ℂ^{n} where the first λ_{1} coordinates are equal, the next λ_{2} coordinates are equal, etc. In this paper, we study subspace arrangements X_{λ} consisting of the union of translates of E_{λ} by the symmetric group. In particular, we focus on determining when X_{λ} is Cohen-Macaulay (CM). This is inspired by previous work of the third author coming from the study of rational Cherednik algebras and which answers the question positively when all parts of λ are equal. We show that X_{λ} is not CM when λ has at least four distinct parts, and handle a large number of cases when λ has two or three distinct parts. Along the way, we also settle a conjecture of Sergeev and Veselov about the Cohen-Macaulayness of algebras generated by deformed Newton sums. Our techniques combine classical techniques from commutative algebra and invariant theory; in many cases, we can reduce an infinite family to a finite check which can sometimes be handled by computer algebra.

Original language | English |
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Pages (from-to) | 2104-2126 |

Number of pages | 23 |

Journal | International Mathematics Research Notices |

Volume | 2016 |

Issue number | 7 |

DOIs | |

State | Published - 1 Jan 2016 |

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