Timeline for Reference for restriction of a simple module over a splitting field to a smaller field?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 7, 2016 at 14:10 | answer | added | Glasby | timeline score: 2 | |
| Mar 16, 2012 at 16:20 | vote | accept | Jim Humphreys | ||
| Mar 14, 2012 at 22:45 | comment | added | Jim Humphreys | @George: My initial formulation was a little loose, in keeping with the somewhat convoluted quewtions I was being asked. So I've tried to tighten the assumptiuons. (My language "restriction of scalars" isn't precise, but imitates terminology used by Weil and others for algebraic group structure relative to field extensions. It's probably not helpful here.) | |
| Mar 14, 2012 at 22:41 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
added 991 characters in body
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| Mar 14, 2012 at 9:36 | answer | added | Geoff Robinson | timeline score: 7 | |
| Mar 14, 2012 at 0:44 | comment | added | George McNinch | Maybe you mean: the composition factors $S$ of $N$ as $F[G]$ module can have $\dim_F S > \dim_E M$. | |
| Mar 14, 2012 at 0:41 | comment | added | George McNinch | Just to make sure I understand what you mean: if $M$ is a simple module for $E[G]$, and $N$ is the $F[G]$-module obtained by "restriction scalars", then $\dim_F N = [E:F] \dim_E M$, right? I didn't quite know what you meant by "...typically has larger dimension..." -- it seems that it has larger dimension whenever $E \ne F$. | |
| Mar 13, 2012 at 23:01 | history | asked | Jim Humphreys | CC BY-SA 3.0 |