Timeline for A question about multiplication in $G(\mathbb{C}((t)))$ and Affine Grassmannians
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| S Jul 10, 2013 at 13:09 | history | bounty ended | CommunityBot | ||
| S Jul 10, 2013 at 13:09 | history | notice removed | CommunityBot | ||
| Jul 2, 2013 at 12:27 | history | edited | Oliver Straser | CC BY-SA 3.0 |
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| Jul 2, 2013 at 12:04 | history | edited | Oliver Straser | CC BY-SA 3.0 |
added 448 characters in body
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| S Jul 2, 2013 at 11:59 | history | bounty started | Oliver Straser | ||
| S Jul 2, 2013 at 11:59 | history | notice added | Oliver Straser | Authoritative reference needed | |
| Jun 22, 2013 at 12:19 | comment | added | Allen Knutson | (Oops, not $H^0$, $H^{top}$.) | |
| Jun 21, 2013 at 12:07 | comment | added | Oliver Straser | My question somehow breaks down to the following: Given $h\in G(\mathcal{O})$, $\lambda,\mu,\nu$ and $w$ as above. I would like to show: $\lambda h \mu\in G(\mathcal{K})^\nu\Leftrightarrow$ there exists $h_1,h_2\in G(\mathcal{O})$, s.t. $h_2 \cdot w\cdot h_2=h$ and $\lambda h_1\lambda^{-1}\in G(\mathcal{O})$ as well as $\mu^{-1} h_2\mu\in G(\mathcal{O})$. I was hoping that some kind "Bruhat decomposition" would yield such a result. | |
| Jun 21, 2013 at 11:22 | comment | added | Allen Knutson | Geometric Satake says that the $H^0$ of the $\nu$-fiber of $m$ should be the intertwining space $Hom(V_\lambda \otimes V_\mu,V_\nu)$. If I'm reading it right, your second question is about the PRV conjecture, which only said (in this language) that that fiber is nonempty, not that it's irreducible. I think it'll be reducible for e.g. $G=SL(3)$, $\lambda = \mu = \nu =$ the highest root $= \rho$. | |
| Jun 21, 2013 at 8:55 | history | asked | Oliver Straser | CC BY-SA 3.0 |