Timeline for To what extent does the $(\mathfrak{g},K_{\infty})$ module determines the automorphic representation?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Jan 9, 2023 at 23:24 | comment | added | Marsault Chabat | Ok thank you very much! | |
| Jan 9, 2023 at 22:11 | comment | added | Peter Humphries | No, you can have two automorphic representations that are quadratic twists of one another and have the same local components at 50% of their places. And no, the weight of a discrete series is not contained in the central character, except that there is a compatibility $\omega(-1) = (-1)^k$. | |
| Jan 9, 2023 at 21:17 | comment | added | Marsault Chabat | Hi Peter, I have a question on your answer of 1). If I assume that the two cuspidal representations also share one of (resp almost all, all) their principal series component? Can we then say that they are the same? Also, the weight $k$ you're talking about is contained in the $\omega$ character right? | |
| Jan 6, 2019 at 18:59 | vote | accept | Wenzhe | ||
| Jan 6, 2019 at 4:37 | history | answered | Peter Humphries | CC BY-SA 4.0 |