The combinatorics of C*-fixed points in generalized Calogero-Moser spaces and 
Hilbert schemes

Przeździecki, Tomasz

doi:10.1016/j.jalgebra.2020.04.003

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The combinatorics of C^*-fixed points in generalized Calogero-Moser spaces and Hilbert schemes

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Przeździecki, Tomasz
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1016/j.jalgebra.2020.04.003
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Citation

Przeździecki, T. (2020). The combinatorics of C^*-fixed points in generalized Calogero-Moser spaces and Hilbert schemes. Journal of Algebra, 556, 936-992. doi:10.1016/j.jalgebra.2020.04.003.

Cite as: https://hdl.handle.net/21.11116/0000-000B-26C2-F

Abstract

In this paper we study the combinatorial consequences of the relationship
between rational Cherednik algebras of type $G(l,1,n)$, cyclic quiver varieties
and Hilbert schemes. We classify and explicitly construct $\mathbb{C}^*$-fixed
points in cyclic quiver varieties and calculate the corresponding characters of
tautological bundles. Furthermore, we give a combinatorial description of the
bijections between $\mathbb{C}^*$-fixed points induced by the Etingof-Ginzburg
isomorphism and Nakajima reflection functors. We apply our results to obtain a
new proof as well as a generalization of the $q$-hook formula.