Timeline for Why are Trace characters regular functions on the Bernstein Variety?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 18, 2017 at 1:11 | vote | accept | Alexander | ||
| Feb 15, 2017 at 20:25 | answer | added | LSpice | timeline score: 1 | |
| Feb 14, 2017 at 3:39 | comment | added | LSpice | Oh, right. I'm a supercuspidals guy, and I just plumb forgot about parabolic induction. I think that Theorem 2, p. 233, of van Dijk's "Computation of certain induced characters of $\mathfrak p$-adic groups" will do it, though it may be overkill. | |
| Feb 13, 2017 at 22:42 | comment | added | Alexander | @LSpice Right, but I guess in general, one is considering something like $\mathrm{tr} I_P^G( \pi \otimes \chi)(f)$ and it wasn't clear to me how to deal with this induction. | |
| Feb 13, 2017 at 22:32 | comment | added | LSpice | It's way less interesting than you think: the analytic structure on the Bernstein spectrum comes from twisting by unramified characters. If $f$ is the characteristic function of a coset of a compact, open subgroup, then $\operatorname{tr} (\pi \otimes \chi)(f)$ equals $\chi(g)\operatorname{tr} \pi(f)$ for any $g$ in the support of $f$. The general result follows by writing an arbitrary $f$ as a combination of such characteristic functions. | |
| Feb 13, 2017 at 22:24 | history | asked | Alexander | CC BY-SA 3.0 |