Timeline for Linearisation of a group
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Nov 4, 2013 at 7:42 | comment | added | Leox | Oh Yes, the Krull dimension of $C[V]^{SL_2}$ equals $\dim V-1 $ and then the asymptotic growth rate for its Hilbert series leading term is almost $O(n^{\dim V-2}),$ like as for one derivation. In other words, a finite group has not enough elements (hence $C[V]^G$ is too big) and it is main reason why $C[V]^G \neq C[V]^D$. Thank you for the clarification. | |
| Nov 4, 2013 at 6:52 | comment | added | Qiaochu Yuan | @Leox: when I appeal to Molien's theorem. | |
| Nov 4, 2013 at 6:49 | comment | added | Leox | Thank you. If I understood correctly you estimate an asymptotic growth rate for the leading term of the two Hilbert series. The first one for the graded algebra $C[V]^G$ and the second one is for $C[V]^D.$ The rates are different, therefore $C[V]^G \neq C[V]^D.$ Please explane again where did you use that $G$ is a finite group? Why these reasoning does't pass for $G=SL_2(C).$? | |
| S Nov 4, 2013 at 6:27 | history | answered | Qiaochu Yuan | CC BY-SA 3.0 | |
| S Nov 4, 2013 at 6:27 | history | made wiki | Post Made Community Wiki by Qiaochu Yuan |