Timeline for Restriction of scalars for the adjoint representation of $SL_2(\mathbb F_q)$
Current License: CC BY-SA 3.0
5 events
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| Nov 8, 2014 at 14:53 | comment | added | Venkataramana | @Michor: thank you. After reading the ans carefully, I see that you were looing at the 3 dimensional adjoint module. | |
| Nov 8, 2014 at 8:54 | comment | added | Peter Mueller | @Venkataramana: So do I. The matrices $A$ are clearly elements from $V$, and as I said in the proof, an orbit of $G$ through $A$ is the conjugacy class $A^G$ ($=\{g^{-1}Ag\;|\;g\in G\}$). If $A$ lies in a submodule $W$, then $A^G\subseteq W$, and then also the $\mathbb F_p$ span of $A^G$ is contained in $W$. But the latter is $V$ for the given matrices $A$. | |
| Nov 8, 2014 at 2:47 | comment | added | Venkataramana | Are you looking at the two dimensional rep of $V$? Joel looks at the three dimensional adjoint representation $V$. | |
| Nov 7, 2014 at 23:44 | history | edited | Peter Mueller | CC BY-SA 3.0 |
added 104 characters in body
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| Nov 7, 2014 at 20:57 | history | answered | Peter Mueller | CC BY-SA 3.0 |