Timeline for What are the equations for $SL_3/SL_2$?

10 events

when toggle format	what		by	license	comment
Dec 28, 2018 at 22:03	history	edited	user44191	CC BY-SA 4.0	deleted 5 characters in body
Dec 28, 2018 at 21:20	history	edited	user44191	CC BY-SA 4.0	Expanded on the geometric/group-theoretic idea in YCor's comment
Dec 28, 2018 at 8:08	comment	added	YCor		In a more group-theoretic point of view: $SL(V)$ acts linearly on $V\oplus V^$. If $\dim(V)\ge 3$, this action has exactly 5 orbits: $\{(0,0)\}$, $(V-\{0\})\oplus\{0\}$, $\{0\}\oplus (V^-\{0\})$, the set of pairs $(v,\ell)$ such that $v\neq 0$, $\ell(v)=0$, and finally the the set of pairs $(v,\ell)$ such that $\ell(v)\neq 0$. For this latter orbit, the point stabilizer of $(v,\ell)$ preserves the decomposition $Kv\oplus \mathrm{Ker}(\ell)$, fixes $v$ and acts on the hyperplane as an element of determinant 1, so the orbit of $(v,\ell)$ is the required homogeneous space.
Dec 28, 2018 at 4:54	history	edited	user44191	CC BY-SA 4.0	added 27 characters in body
Dec 28, 2018 at 4:31	vote	accept	Question Machine
Dec 28, 2018 at 4:08	history	edited	user44191	CC BY-SA 4.0	added 111 characters in body
Dec 28, 2018 at 3:25	history	edited	user44191	CC BY-SA 4.0	Finished an edit accidentally left half-done, added a new idea
Dec 28, 2018 at 3:20	history	edited	user44191	CC BY-SA 4.0	Finished an edit accidentally left half-done
Dec 28, 2018 at 3:12	history	edited	GH from MO	CC BY-SA 4.0	added 4 characters in body
Dec 28, 2018 at 3:11	history	answered	user44191	CC BY-SA 4.0