Timeline for Highest weights of the restriction of an irreducible representation of a simple group to a Levi subgroup
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 23, 2012 at 9:54 | comment | added | Sasha | @Misha, Thanks a lot! In fact I already managed to circumvent the problem with branching that I had at that time, but I am still interested in the question. Can you give me a reference to a precise statement about the branching in the paper? I looked the paper through but haven't noticed "branching" mentioned in the text. | |
| Dec 21, 2012 at 5:33 | comment | added | Misha | Sasha, I do not know if you are still interested in the question, but this [www2.math.umd.edu/~tjh/HKMm.pdf] might be helpful. | |
| Aug 17, 2010 at 14:51 | answer | added | Allen Knutson | timeline score: 2 | |
| Aug 17, 2010 at 5:32 | comment | added | Victor Protsak | General case may be considerably more involved than what happens in type A. For your modified question, Guillemin-Sjamaar would be a natural place to check. However, I've spent enough time on your problem with not even symbolic gain and I don't have any incentive to think about it further. – Victor Protsak 2010-08-17 04:36:22Z UTC | |
| Aug 17, 2010 at 5:30 | comment | added | Victor Protsak | I guess in type A one can use Gelfand-Tsetlin rules to deduce the restriction. For example, if $G=GL_3, L=GL_2\times C^*$ (the maximal parabolic corresponding to the root $\alpha_2$) these rules show that highest weights of $(V_G^\lambda)_{|L}$ all lie in $Conv(\lambda,s_2\lambda,s_2s_1\lambda,\lambda+s_2s_1\lambda - s_2\lambda)$. I would like to have something similar in general - a universal collection of elements in $\mathbb{Z}[W]$, so that every highest weight of $(V_G^\lambda)_{|L}$ is contained in the convex envelope of these elements applied to $\lambda$. –Sasha 2010-08-17 03:56:43Z UTC | |
| Aug 17, 2010 at 1:59 | comment | added | Allen Knutson | Note that not all weights in that convex hull occur -- only the ones that differ from $\lambda$ by an element of the root lattice. This gets worse for other branching problems, though maybe not yours. | |
| Aug 16, 2010 at 22:07 | answer | added | Jim Humphreys | timeline score: 2 | |
| Aug 16, 2010 at 21:15 | history | asked | Sasha | CC BY-SA 2.5 |