Timeline for Parametrization of the admissible dual
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 12, 2017 at 16:29 | comment | added | paul garrett | Your revised question seems to ask how we know the subrepresentation theorem for spherical representations. To my perception, this is still a very big question, and I do not know how to answer, outside of examples in the rank-one case, where asymptotics and other features of ordinary differential equations play a key role. In higher rank, the analogue is the appendix in Casselman-Milicic, expanding a paper of Deligne on the PDE analogue. | |
| Oct 12, 2017 at 7:55 | history | edited | YCor |
edited tags
|
|
| Oct 12, 2017 at 5:52 | comment | added | Desiderius Severus | @paulgarrett I have added some precisions in my question, that I believe I do not understand enough myself to ask it in a correct way. Im a interested in archimedean local duals and I would like to understand the isomorphism. Has it anything to do with the "infinitesimal equivalence" notion? | |
| Oct 12, 2017 at 5:50 | history | edited | Desiderius Severus | CC BY-SA 3.0 |
Admissible not spherical, and precision that I am interested in the archimedean case
|
| Sep 26, 2017 at 19:52 | comment | added | paul garrett | Well, an (irreducible admissible) spherical repn imbeds (by the Casselman subrepn thm) in a (spherical) principal series that is unique mod $W$, and no non-isomorphic spherical repns imbed into the same principal series. I don't know what you mean by "explicit"... For the full dual, it can happen that two distinct irreducible imbed into the same principal series, messing up the bijection. Not so much "contained in $A$" as perhaps "dual", maybe? And we really do need the complexification, because (for example) spherical repns need not be unitary, etc. | |
| Sep 26, 2017 at 9:00 | history | asked | Desiderius Severus | CC BY-SA 3.0 |