Timeline for What is the "weight" of an automorphic form for $\mathrm{PGL}_2$?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 10 at 14:02 | comment | added | Kimball | Well, "automorphic" is only for global representations. Try smooth or admissible. Yyou might start by looking at the books of Gelbart (less detailed) or Bump (more detailed), which discuss the global and local pictures. | |
| Mar 9 at 21:45 | comment | added | HASouza | @Kimball I see, so what I should search for is something along the lines of "classification of irreducible automorphic representations" of $\operatorname{PGL}_2(\mathbb{R})$ and $\operatorname{PGL}_2(\mathbb{C})$? | |
| Mar 9 at 20:20 | comment | added | Kimball | Without reading your question in detail, the weight of $\pi$ is however the authors choose to describe the archimedean representation $\pi_\infty$. E.g., for a holomorphic Hilbert eigenform, $\pi_\infty$ is a discrete series representation parametrized by a tuple of integers, the classical weight $(k_1, \dots, k_n)$. | |
| Mar 9 at 16:30 | history | edited | YCor | CC BY-SA 4.0 |
formatting
|
| Mar 9 at 16:26 | history | asked | HASouza | CC BY-SA 4.0 |