Timeline for Bounding $p$-adic characters and Jacquet-Langlands transfert
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 1, 2018 at 13:49 | vote | accept | Desiderius Severus | ||
| Dec 18, 2016 at 9:58 | comment | added | Desiderius Severus | @JudithLudwig Could we lift a bound on the character associated to $\pi_{SL_2(\mathbf{Q}_p)}$ to a bound on the character associated to $\pi$, representation on $GL_2$? | |
| Mar 24, 2016 at 22:54 | history | bounty ended | Desiderius Severus | ||
| Mar 24, 2016 at 22:54 | vote | accept | Desiderius Severus | ||
| Dec 18, 2016 at 9:58 | |||||
| Mar 24, 2016 at 22:54 | comment | added | Desiderius Severus | @LSpice Thanks for the references, especially leading me towards DeBacker's thesis. | |
| Mar 24, 2016 at 22:53 | comment | added | Desiderius Severus | @JudithLudwig Thank you for those explanation, they seems to do the job for my purposes for now. The main point was the uniformly bounded number of representations in the decomposition of the restriction, and it is donne by Shelstad as mentioned in Lansky and Raghuram's article ! | |
| Mar 24, 2016 at 14:36 | comment | added | Judith Ludwig | @ L Spice: I think it holds for $p=2$. you are right, the reference I mentioned does assume $p=2$, however in Labesse and Langlands, L-Indistinguishability for SL(2), $p$ is arbitrary. Also if you believe that the size of the $L$-packet is in bijection with the component group of the centralizer of the associated projective Weil-Deligne representation it is an exercise to compute that the only possible sizes are of 1,2 or 4. | |
| Mar 24, 2016 at 14:03 | comment | added | LSpice | Another helpful reference for decomposition is Moy and Sally, Supercuspidal representations of $\mathrm{SL}_n$ over a $p$-adic field: the tame case (MR). Are you sure that your statement that your $n$ divides $4$ is true even for $p = 2$? (I don't know that it isn't, only that I am automatically suspicious.) | |
| Mar 24, 2016 at 13:50 | history | answered | Judith Ludwig | CC BY-SA 3.0 |