Timeline for Simply connected algebraic groups and reductive subgroups of maximal rank
Current License: CC BY-SA 3.0
4 events
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| Apr 4, 2013 at 22:48 | comment | added | Jim Humphreys |
P.S. Looking further at your example, I'm probably more confused than before. The root lattices for $G$ and for $H=H'$ are not the same even though the maximal torus is the same for both. What is the index of each root lattice in the full weight lattice for $G$, assumed to be $X(T)$? For a simply connected $D_4$ it's certainly 4. I have to check Bourbaki's table again, but my computation doesn't seem to agree with yours. It's confusing to me because of all the factors 1/2 that occur.
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| Apr 4, 2013 at 21:43 | history | edited | Marc van Leeuwen | CC BY-SA 3.0 |
corrected index calculation
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| Apr 4, 2013 at 20:28 | comment | added | Jim Humphreys | @Marc: Thanks for pointing out this example, which I had skipped over too quickly. I'm not sure whether any predictable pattern exists, especially for these non-irreducible subsystems. In a way that's simpler, since there seems to be no conceptual reason for uniformity in thuis indirect method of constructing reductive subgroups of maximal rank. | |
| Apr 4, 2013 at 16:40 | history | answered | Marc van Leeuwen | CC BY-SA 3.0 |