Automorphisms of complex reflection groups
| dc.creator | Marin, Ivan | |
| dc.creator | Michel, Jean | |
| dc.date | 2007-01-09 | |
| dc.date | 2009-03-12 | |
| dc.date.accessioned | 2026-07-07T12:51:42Z | |
| dc.date.available | 2026-07-07T12:51:42Z | |
| dc.description | Let $G\subset\GL(\BC^r)$ be a finite complex reflection group. We show that when $G$ is irreducible, apart from the exception $G=\Sgot_6$, as well as for a large class of non-irreducible groups, any automorphism of $G$ is the product of a central automorphism and of an automorphism which preserves the reflections. We show further that an automorphism which preserves the reflections is the product of an element of $N_{\GL(\BC^r)}(G)$ and of a "Galois" automorphism: we show that $\Gal(K/\BQ)$, where $K$ is the field of definition of $G$, injects into the group of outer automorphisms of $G$, and that this injection can be chosen such that it induces the usual Galois action on characters of $G$, apart from a few exceptional characters; further, replacing if needed $K$ by an extension of degree 2, the injection can be lifted to $\Aut(G)$, and every irreducible representation admits a model which is equivariant with respect to this lifting. Along the way we show that the fundamental invariants of $G$ can be chosen rational. | |
| dc.identifier | https://arxiv.org/abs/math/0701266 | |
| dc.identifier | http://arxiv.org/abs/math/0701266 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223075 | |
| dc.subject | Representation Theory | |
| dc.subject | Group Theory | |
| dc.subject | 20F55, 20F28, 20C99 | |
| dc.title | Automorphisms of complex reflection groups | |
| dc.type | text |