Nonlinearizable actions of dihedral groups on affine space

Masuda, Kayo

doi:10.1090/S0002-9947-03-03405-6

Nonlinearizable actions of dihedral groups on affine space
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Trans. Amer. Math. Soc. 356 (2004), 3545-3556 Request permission

Abstract:

Let $G$ be a reductive, non-abelian, algebraic group defined over $\mathbb {C}$. We investigate algebraic $G$-actions on the total spaces of non-trivial algebraic $G$-vector bundles over $G$-modules with great interest in the case that $G$ is a dihedral group. We construct a map classifying such actions of a dihedral group in some cases and describe the spaces of those non-linearizable actions in some examples.

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