Timeline for Is there any way to determine the "effeciency" of Jantzen's sum formula?
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| Feb 6, 2014 at 14:33 | comment | added | Jim Humphreys | @David: Yes, I meant to get into more details about what some of those methods involve. I should also mention that Jantzen's earlier method, with a bound on $p$, uses some of the same ideas about contravariant forms as Wong did. So the general theory is somewhat connected, though practical methods diverge. | |
| Feb 6, 2014 at 13:29 | comment | added | David Stewart | In terms of software, you should definitely have a play with Steve Doty's Weyl module package for GAP. Frank Luebeck wrote a paper `Small representations of finite Chevalley groups' where he says he actually computes the Jantzen filtration explicity, though these calcs do not appear in the paper---so maybe send him an email. Also worth noting that I wrote a paper with Alison Parker, BLMS to appear, where we used Jantzen's sum formula to bound the number of composition factors in Weyl modules with restricted heads. There may be something in there relevant to your question. | |
| Feb 6, 2014 at 13:24 | comment | added | Jim Humphreys | @Tobias: I haven't done much computing of special cases myself, but my understanding is that the older computational methods of people like Gilkey and Seitz (going back to work of Wong, Burgoyne) deal more quickly with small ranks, small primes, small weights. The idea is to start with integral forms using a Chevalley basis. It's not clear to me what current software exists, but a number of methods have been developed over the years. Of course, none of this sheds much light on the deeper theoretical questions. | |
| Feb 6, 2014 at 9:10 | comment | added | Tobias Kildetoft | I definitely agree that the sum formula should not be regarded solely as a computational tool. But on the other hand it is certainly also useful as such, and when using it as such, the types of bounds I am looking for would be useful. Of course, it might well be that nobody has even tried finding such, as they might not be much use in theoretical work. | |
| Feb 5, 2014 at 14:02 | history | answered | Jim Humphreys | CC BY-SA 3.0 |