Timeline for Why admissible representations?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Nov 1, 2020 at 7:24 | comment | added | Peter Humphries | @Kimball Indeed, local newforms lie in a $K$-type that occurs with multiplicity one: arxiv.org/abs/2009.08571 | |
| Nov 1, 2020 at 4:23 | comment | added | Kimball | You won't probably have a nice theory of new/test vectors or nice models, like unique Whittaker models. | |
| Nov 1, 2020 at 4:11 | comment | added | Will Sawin | Isn't it mainly because we're interested in the irreducible smooth representations, and the admissible representations have all the useful finiteness properties of irreducible smooth representations but are closed under more operations? | |
| Nov 1, 2020 at 3:43 | comment | added | LSpice | Counterexamples to what? My understanding is that considering admissible representations is like considering reductive groups: they are numerous enough that they have nice heredity properties, like your (3), and small enough that they are accessible through more familiar means, like your (1). Of course the set of all, say, smooth representations satisfies your (2)–(3), but it's too big to hope to get a handle on it. (You'll find non-admissible counterexamples to (1) in abundance, because that's practically the definition of admissibility.) | |
| Nov 1, 2020 at 3:42 | history | edited | LSpice | CC BY-SA 4.0 |
Proofreading
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| Nov 1, 2020 at 3:16 | history | asked | Wirdspan | CC BY-SA 4.0 |