Timeline for what information of a representation was killed by Jacquet functor?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Apr 27, 2010 at 13:14 | comment | added | Emerton | But the question does say $(g,K)$-module ... . | |
| Apr 27, 2010 at 12:38 | history | edited | Kevin Buzzard | CC BY-SA 2.5 |
added 244 characters in body
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| Apr 27, 2010 at 12:37 | comment | added | Kevin Buzzard | Hah! He didn't say what base field he was over! | |
| Apr 27, 2010 at 12:21 | comment | added | Emerton | Kevin, This question is about Harish-Chandra modules, i.e. real groups, not p-adic groups. There are no supercuspidals ... . | |
| Apr 27, 2010 at 8:43 | comment | added | Kevin Buzzard | This is very vague (but then again your question is also vague)---perhaps for GL_n on the Galois side, the Jacquet module sees something like the Frobenius action on the inertia-invariant vectors, so to see the rest of $V$ (assuming $V$ is irreducible) you'll need to know the inertia action, which somehow boils down to seeing the type of $V$. So perhaps you need to know "enough about the action of $K$". | |
| Apr 27, 2010 at 8:33 | history | answered | Kevin Buzzard | CC BY-SA 2.5 |