Timeline for Chevalley–Shephard–Todd theorem
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
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| Nov 22, 2017 at 21:37 | answer | added | David E Speyer | timeline score: 10 | |
| Feb 20, 2017 at 6:04 | answer | added | Joshua P. Swanson | timeline score: 7 | |
| Jul 24, 2011 at 2:37 | answer | added | David Wehlau | timeline score: 2 | |
| Jul 19, 2010 at 10:41 | comment | added | Jim Humphreys |
Probably the most thorough coverage, with full references (Serre's improvement of Chevalley's statement, Springer's lecture notes, Borel's historical essays, etc.) is given by G.I. Lehrer and D.E. Taylor in Unitary Reflection Groups (Cambridge, 2009). Like most people they work over $\mathbb{C}$, leaving aside the more delicate question of what remains true over more general fields mentioned here by Victor Protsak. This book treats Shephard-Todd theory and later developments in good detail.
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| Jul 19, 2010 at 10:00 | vote | accept | Roman Fedorov | ||
| Jul 19, 2010 at 9:57 | comment | added | Roman Fedorov | Chevalley only gives the proof for reflection groups but he only uses that a reflection fixes a hyperplane. | |
| Jul 19, 2010 at 8:19 | comment | added | Victor Protsak | "Invariant theory of finite groups" by Mara Neusel and Larry Smith contains the proof. Note, however, that while the "inverse" implication holds in general by homological algebra, the "direct" implication fails in positive characteristic. | |
| Jul 19, 2010 at 7:52 | comment | added | user717 | An additional question: Is it correct that Chevalley only gave a proof for reflection groups (reflection = pseudo-reflection of order 2) in this paper and that Serre later realized that the proof also works for pseudo-reflection groups? | |
| Jul 19, 2010 at 7:33 | answer | added | Torsten Ekedahl | timeline score: 21 | |
| Jul 19, 2010 at 6:42 | history | asked | Roman Fedorov | CC BY-SA 2.5 |