Timeline for On a theorem of Kazhdan
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 25, 2015 at 4:55 | comment | added | Dmitry Vaintrob | Ah sorry, thought you were twisting by a character of the Levi (which would not affect the dimension... your current question makes a lot more sense). | |
| Mar 25, 2015 at 3:54 | comment | added | user64433 | of the mirabolic of the upper $GL(2)$, not the full Levi. Also, I cannot find the statement which says the twisted Jacquet functor is admissible. Do you know where I can find this? | |
| Mar 25, 2015 at 3:52 | comment | added | user64433 | Thanks for your answer. But I have a question on part (2) above. If $\theta$ is trivial, I know that the standard Jacquet functor $V_U$ is an admissible representation of the Levi. But, if $\theta$ is not trivial, the twisted Jacquet functor $V_{U,\theta}$ is not even a representation of the full Levi. Think about the GL(3) case. Let $P$ be the parabolic of type (2,1), i.e., the Levi is $GL(2)\times GL(1)$, with $GL(2)$ at the left upper corner. If $\theta$ is the character defined on the (2,3) position of the unipotent, then $V_{U,\theta}$ is just a representation of the mirabolic | |
| Mar 24, 2015 at 21:32 | history | edited | Dmitry Vaintrob | CC BY-SA 3.0 |
minor correction
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| Mar 24, 2015 at 21:22 | history | edited | Dmitry Vaintrob | CC BY-SA 3.0 |
minor edit
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| Mar 24, 2015 at 21:16 | history | answered | Dmitry Vaintrob | CC BY-SA 3.0 |