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arXiv · 1806.05704

Ansatz for $(-1)^{n-1}\nabla p_n$

Soumya Dipta Banerjee·Mahir Bilen Can·Adriano Garsia
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Abstract

We construct a special family of equivariant coherent sheaves on the Hilbert scheme on $n$-points in the affine plane. The equivariant Euler characteristic of these sheaves are closely related to the symmetic functions $(-1)^{n-1} \nabla p_n$. We prove a higher cohomology vanishing result of these sheaves. It follows from the Bridgeland-King-Reid correspondence that there is an effective $S_n$ module underlying the aforementioned family of symmetric functions.

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Soumya Dipta Banerjee, Mahir Bilen Can, Adriano Garsia. 2018-06-14. Ansatz for $(-1)^{n-1}\nabla p_n$. https://arxiv.org/abs/1806.05704

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