Timeline for Conductor of monomial forms with trivial nebentypus
Current License: CC BY-SA 2.5
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| Mar 9, 2010 at 12:40 | comment | added | Kevin Buzzard | In some sense I'm not sure that the representation theory facts shed any more light on the situation---they're just a translation of the Galois comments above to the automorphic side. For example, the statement that the Steinberg is (up to unram twist) the only smooth admiss rep of GL_2(Q_p) with unramified central char and conductor p is just a trivial consequence of the local Langlands conjectures and a calculation on the Galois side very analogous to the above (but with Weil-Deligne groups instead of Galois groups, so you're allowed a monodromy operator). Read any intro to LL for GL_n/Q_p! | |
| Mar 9, 2010 at 11:51 | comment | added | Idoneal | Yes, the Galois side is a slightly more familiar territory for me and this proof is quite clear. Thanks. I shall appreciate very much, nevertheless, if you (or anyone) can suggest some references for the representation theory facts used in the earlier arguments. I looked up Bump's text book but that seems not to be adequate. | |
| Mar 9, 2010 at 10:26 | history | answered | Kevin Buzzard | CC BY-SA 2.5 |