Timeline for Kostant partition function: asymptotics and specifics
Current License: CC BY-SA 3.0
5 events
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| Jul 21, 2012 at 17:02 | comment | added | Chuck Hague | I made a mistake in my initial comment, which I hopefully fixed in my later comment (unless it's still wrong) -- oh for an edit window on comments. I think the point is that for any weight $\lambda \geq 0$ and dominant $\mu \gg 0$ the dimension of the $\mu-\lambda$-weight space of $H^0(\mu)$ is given by $\mathfrak P(\lambda)$, which isn't actually a statement about Steinberg modules but about weight spaces of the zero Verma module. | |
| Jul 21, 2012 at 14:47 | comment | added | Jim Humphreys | @Chuck: I think your newer statement of Jantzen's result in the comments is still out of focus, since he isn't actually looking at the weights of a Steinberg module but instead tensors it with its highest weight. (I tried to explain this in my own added remarks.) | |
| Jul 20, 2012 at 17:36 | history | edited | Chuck Hague | CC BY-SA 3.0 |
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| Jul 20, 2012 at 15:22 | history | edited | Chuck Hague | CC BY-SA 3.0 |
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| Jul 19, 2012 at 17:17 | history | answered | Chuck Hague | CC BY-SA 3.0 |