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Feb 7 at 22:28 history edited Dr. Evil
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Feb 6 at 23:38 comment added Dr. Evil Ah yes. I was thinking about GL. It is corrected now. Thanks @Sasha
Feb 6 at 23:38 history edited Dr. Evil CC BY-SA 4.0
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Feb 6 at 7:45 comment added Sasha You seem to forget the relation $a_{11} + a_{22} = 0$ for $\mathrm{SL}_2$. If you take it into account, the GIT quotient is $\mathbb{A}^2$.
Feb 6 at 7:26 comment added მამუკა ჯიბლაძე For $\mathfrak{sl}_3$ it is $\mathbb C[a_{11},a_{33},a_{12}a_{21},a_{23}a_{32},a_{13}a_{31}, a_{12}a_{23}a_{31},a_{21}a_{13}a_{32}]$ i. e. $\mathbb C[x,y,z,t,u,v,w]/(ztu-vw)$
Feb 6 at 5:59 history edited Dr. Evil CC BY-SA 4.0
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Feb 6 at 5:45 history asked Dr. Evil CC BY-SA 4.0