The combinatorics of \(C^\ast \)-fixed points in generalized Calogero-Moser spaces and Hilbert schemes. (English) Zbl 1454.16019
Summary: 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 \(\mathbb{C}^\ast \)-fixed points in cyclic quiver varieties and calculate the corresponding characters of tautological bundles. Furthermore, we give a combinatorial description of the bijections between \(\mathbb{C}^\ast \)-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.
MSC:
| 16G20 | Representations of quivers and partially ordered sets |
| 05E10 | Combinatorial aspects of representation theory |
| 20C08 | Hecke algebras and their representations |
Keywords:
rational Cherednik algebras; Hilbert schemes; Nakajima quiver varieties; Calogero-Moser space; \(q\)-hook formula; wreath Macdonald polynomials; degenerate affine Hecke algebrasReferences:
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