Timeline for Computing explicit matrix coefficients
Current License: CC BY-SA 4.0
5 events
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| Oct 18, 2020 at 14:41 | comment | added | Kimball | You can compute the matrix coefficients, at least in the unramified case as Paul says, if you choose v, w to be (normalized) Whittaker newvectors. E.g. see Godement's notes on JL. Is this what you're looking for? I'm not sure I completely understand the question. | |
| Oct 18, 2020 at 13:30 | comment | added | Desiderius Severus | These matrix coefficients computations and convergence issues may be written somewhere, and I may be underlooking many of the papers I read. However, I have the feeling that computations are either done explicitly with other aims in mind (viz. L-functions or analytic issues, e.g. Ralf Schmidt's notes) or stay in a very general framework concerning matrix coefficients (viz. orthogonality or traces formulas, e.g. Peter-Weyl or Bekka-de la Harpe ; or more general groups, e.g. Tadic) I want to understand precisely how to cope with matrix coefficients, if this can help clarifying the OP. | |
| Oct 18, 2020 at 13:19 | comment | added | Desiderius Severus | @PaulBroussous Thanks! My knowledge in representation theory is limited and this is why I am asking for some guidance. I have the feeling that a lot is known and for sure what I want is scattered somewhere. For instance, I bet I just aim at exemplifying Tadic's paper on the Fell topology to the case of GL(2). However, even after having read some of Casselman's introductory notes and book, and just went through MacDonald, I'm still uneasy. I know standard realizations of principal series, definition of matrix coefficients, but what about explicit choice of inner product, test vectors, etc.? | |
| Oct 18, 2020 at 11:15 | comment | added | Paul Broussous | A lot has been known for a long time for unramified representations of p-adic groups (representations with a non-zero fixed vector under a good maximal compact subgroup). These representations belong to the principal series. Cf. the works of Macdonald, Casselman ... | |
| Oct 18, 2020 at 2:43 | history | asked | Desiderius Severus | CC BY-SA 4.0 |