Timeline for List of irreducible representations whose weights are in a single Weyl group orbit
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6 events
| when toggle format | what | by | license | comment | |
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| Feb 9, 2015 at 14:52 | comment | added | Allen Knutson | I'm definitely in favor of these being the minuscule representations of $G$, which are the cohomology groups of the cominuscule flag manifolds of the Langlands dual group $G^L$. The co- is for the Langlands duality. (The minuscule flag manifolds are also important; they're the ones that Hodge-degenerate to Stanley-Reisner schemes of order complexes of Bruhat order. I don't know any reason to look at the irreps associated to cominuscule fundamental weights.) | |
| Feb 8, 2015 at 14:52 | comment | added | Jim Humphreys | @ronggang: The usual term is "minuscule" (though "cominuscule" also occurs in some contexts). See the explicit entry in Wikipedia en.wikipedia.org/wiki/Minuscule_representation (but note that the concept comes originally from Bourbaki and others). There is also a recent monograph by Richard Green: Combinatorics of minuscule representations. Cambridge Tracts in Mathematics, 199. Cambridge University Press, Cambridge, 2013 | |
| Feb 7, 2015 at 22:09 | comment | added | ronggang | @ Sasha: Thanks, that's exactly what I want. | |
| Feb 7, 2015 at 22:08 | comment | added | Jim Humphreys | As Sasha points out, this is all standard material. You might also search the Math Overflow pages for questions involving the term "minuscule". | |
| Feb 7, 2015 at 20:50 | comment | added | Sasha | Google for cominuscule representations. | |
| Feb 7, 2015 at 20:20 | history | asked | ronggang | CC BY-SA 3.0 |