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

Gwyn Bellamy; Victor Ginzburg

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

Algebraic Geometry 2015-09-08 v1 Representation Theory

Authors: Gwyn Bellamy , Victor Ginzburg

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.

Keywords

Hilbert scheme of points Calogero-Moser space $SL_2$-action $GL_2$-action orbit closure Procesi bundle character of representation

Cite

@article{arxiv.1509.01674,
  title  = {$SL_2$-action on Hilbert schemes and Calogero-Moser spaces},
  author = {Gwyn Bellamy and Victor Ginzburg},
  journal= {arXiv preprint arXiv:1509.01674},
  year   = {2015}
}

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11 pages

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

Abstract

Keywords

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