Timeline for Connection between global and local notions of a cuspidal representation
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 11, 2019 at 1:58 | comment | added | Will Sawin | As Peter points out, locally supercuspidal implies globally cuspidal, but the converse is not true. The argument is exactly what you give, except we have to observe that $\int_{N(k) \backslash N(\mathbb A_k) } \int_{U} \pi(n) \pi(n_v) w dn_v dn= \int_{N(k) \backslash N(\mathbb A_k) } \pi(n) w dn$ for $U$ a compact open subgroup of $N(k_v)$, which is easy. | |
| Sep 10, 2019 at 22:04 | comment | added | Peter Humphries | Supercuspidal at a finite place implies globally cuspidal, though of course the converse is not true. Other than that, I don't think much else can be said. | |
| Sep 10, 2019 at 20:49 | history | asked | D_S | CC BY-SA 4.0 |