Timeline for Dimension of Unipotent Radicals
Current License: CC BY-SA 3.0
3 events
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| Jan 25, 2013 at 20:01 | comment | added | Jim Humphreys |
@Stanley: Your approach is too complicated. Each of the intermediate Levi subgroups has derived group of simple type $\mathrm{SL}_2$ with a single positive root, so the unipotent radical has dimension $3=4-1$ in both cases. The dimensions of the four possible unipotent radicals for $C_2$ (up to conjugacy) are $0, 3, 3, 4$. Such dimensions are always bounded above by the total number of positive roots, the dimension of a maximal unipotent subgroup. In my example $F_4$`, you get 16 dimensions between 0 and 24, for example, with a few intermediate ones divisible by 4.
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| Jan 25, 2013 at 19:51 | history | edited | Stanley Chang | CC BY-SA 3.0 |
deleted 2 characters in body
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| Jan 25, 2013 at 19:41 | history | answered | Stanley Chang | CC BY-SA 3.0 |