Timeline for on a property of minuscules in weight lattice
Current License: CC BY-SA 3.0
5 events
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| Apr 7, 2017 at 17:52 | comment | added | Jim Humphreys | @Soluble: As suggested by Learn_Math's comment, your "Main fact" 3 isn't true (even with "minimal" replaced by "minuscule"). For example, look at the fundamental weights $\lambda_1, \lambda_6$ for type $E_6$. It may be safest to use case-by-case checking for the coset representatives, though I'd still prefer a uniform proof not relying on affine Weyl groups. | |
| Feb 8, 2017 at 23:23 | comment | added | Jim Humphreys | A small comment on terminology: my use of "minimal" is straightforward relative to the usual partial ordering of dominant weights, but this allows the 0 weight to qualify as minimal (in the coset of the weight lattice corresponding to the root lattice itself). To exclude this rather trivial possibility, the less transparent term "minuscule" is used. | |
| Feb 5, 2017 at 8:42 | comment | added | Learn_Math | Proof of 3 is not clear to me. | |
| Feb 5, 2017 at 7:52 | history | edited | Soluble | CC BY-SA 3.0 |
added 116 characters in body
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| Feb 5, 2017 at 7:45 | history | answered | Soluble | CC BY-SA 3.0 |