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arXiv · 1509.01674

$SL_2$-action on Hilbert schemes and Calogero-Moser spaces

Gwyn Bellamy·Victor Ginzburg
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Abstract

We study the natural $GL_2$-action on the Hilbert scheme of points in the plane, resp. $SL_2$-action on the Calogero-Moser space. We describe the closure of the $GL_2$-orbit, resp. $SL_2$-orbit, of each point fixed by the corresponding diagonal torus. We also find the character of the representation of the group $GL_2$ in the fiber of the Procesi bundle, and its Calogero-Moser analogue, over the $SL_2$-fixed point.

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Gwyn Bellamy, Victor Ginzburg. 2015-09-05. $SL_2$-action on Hilbert schemes and Calogero-Moser spaces. https://arxiv.org/abs/1509.01674

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