Timeline for a question about irreducibility of representations and Kirillov conjecture
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 22, 2014 at 3:55 | vote | accept | user1832 | ||
| Mar 30, 2010 at 15:52 | answer | added | Marty | timeline score: 13 | |
| Mar 30, 2010 at 9:41 | comment | added | Kevin Buzzard | As for your related question: I know one technique that sometimes comes up in the p-adic setting, an analogue of which might work in the real setting: if you can prove that Pi is generated as a G-rep by Pi^K, with K a compact open, and if Pi^K is irreducible as an H(G,K)-module (H the Hecke algebra: note that this is now a question about finite-dimensional representations) then in many cases this is good enough to prove that Pi is irreducible as a G-rep. | |
| Mar 30, 2010 at 9:41 | comment | added | Kevin Buzzard | I have a stupid question! If B is the upper triangular matrices in GL_2(R) and chi_1,chi_2 are two unitary characters of R^*, then I thought that one could make sense of the notion Ind_B^G(chi_1,chi_2) (some normalised induction to make the induced representation unitary), and that this would be an irreducible representation Pi of G. Here's the stupid bit though: if you had asked me, I would have guessed that the restriction of Pi to B (and hence to P) would have been reducible (based on an analogy with finite groups). Am I wrong? | |
| Mar 30, 2010 at 2:38 | history | asked | user1832 | CC BY-SA 2.5 |