Timeline for description of an endomorphism algebra
Current License: CC BY-SA 3.0
3 events
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| Jun 20, 2012 at 16:13 | comment | added | Jim Humphreys | Concerning the permutation module (which is an induced module from a trivial representation), I was just relying on standard tools in characteristic 0: transitivity of induction, Frobenius reciprocity, complete reducibility. Concerning the study of Deligne-Lusztig representations, I'm doubtful that there is a simpler way to study them than found in the existing literature; but of course that's always an open question. | |
| Jun 20, 2012 at 8:33 | comment | added | th.ng | Thank you for your answer, actually, I didn't expect the permutation module $\mathbb{C}[G^F/U^F]$ so be the direct sum of all the induced representations, can you tell me why ? or give me a reference for it ? At the moment, what I want to do isn't clear : I was looking for something to replace the (usual) Hecke algebra, which is related to the unipotent representations of $G^F$, in the case where one considers the other representations (all this is related to Deligne-Lusztig theory and more precisely, instead of studying the varieties $X_w$, I want to have something for $Y_w$). | |
| Jun 17, 2012 at 16:24 | history | answered | Jim Humphreys | CC BY-SA 3.0 |