Coinvariant Algebras of Finite Subgroups of SL(3;C)

Author:

Gomi Yasushi,Nakamura Iku,Shinoda Ken-ichi

Abstract

AbstractFor most of the finite subgroups of SL(3; C) we give explicit formulae for the Molien series of the coinvariant algebras, generalizing McKay's formulae [McKay99] for subgroups of SU(2). We also study the G-orbit Hilbert scheme HilbG(C3) for any finite subgroup G of SO(3), which is known to be a minimal (crepant) resolution of the orbit space C3/G. In this case the fiber over the origin of the Hilbert-Chow morphism from HilbG(C3) to C3/G consists of finitely many smooth rational curves, whose planar dual graph is identified with a certain subgraph of the representation graph of G. This is an SO(3) version of the McKay correspondence in the SU(2) case.

Publisher

Canadian Mathematical Society

Subject

General Mathematics

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Branching Law for the Finite Subgroups of SL4ℂ and the Related Generalized Poincaré Polynomials;Ukrainian Mathematical Journal;2016-03

2. Branching law for finite subgroups of 3 ℂ$\mathbf {SL}_3\mathbb {C}$ and McKay correspondence;Journal of Group Theory;2014-03-01

3. The Lefschetz Elements of Coinvariant Algebras of Binary Polyhedral Groups;Tokyo Journal of Mathematics;2013-12-01

4. Generalized McKay quivers of rank three;Acta Mathematica Sinica, English Series;2013-03-28

5. On G/N-Hilb of N-Hilb;Kyoto Journal of Mathematics;2013-01-01

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