On Cohen-Macaulayness of S_n-invariant subspace arrangements

Understand

Given a partition $\lambda$ of n, consider the subspace $E_\lambda$ of $C^n$ where the first $\lambda_1$ coordinates are equal, the next $\lambda_2$ coordinates are equal, etc.

• In this paper, we study subspace arrangements $X_\lambda$ consisting of the union of translates of $E_\lambda$ by the symmetric group.
• In particular, we focus on determining when $X_\lambda$ is Cohen-Macaulay.
• 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 $\lambda$ are equal.