Timeline for Examples to keep in mind while reading the book 'The Admissible Dual...' by Bushnell and Kutzko and the importance of Interwining of representations
Current License: CC BY-SA 3.0
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| Nov 26, 2016 at 22:34 | comment | added | LSpice | @dulalnarugopal, the relevant point is that the representation is supercuspidal if it is irreducible (since then the extension of a matrix coefficient of the inducing subgroup is a compactly supported matrix coefficient); but Mackey theory allows you to test for irreducibility by looking at intertwining. | |
| May 6, 2016 at 18:06 | comment | added | PL. | Oh, something that it occurs to me I should have said: when you look at $GL_n$ for $n$ prime, you can forget about simple strata and $k_0$. Instead, you just consider fundamental strata of the form $[\mathfrak{A},n,n-1,\beta]$, which are much easier to get used to (in particular, the definition of "fundamental" is easy). I think that this is done for $n=2$ in Bushnell--Henniart, but I can't quite remember how much they prove. Maybe one good, although not quite precise, way of understanding $k_0$ is that it measure how far a stratum is from being fundamental. | |
| May 6, 2016 at 16:46 | vote | accept | MathStudent | ||
| May 5, 2016 at 18:50 | comment | added | PL. | The one I know is Carayol, Représentations cuspidales du groupe linéaire, Proposition 1.5. He cites Howe's paper on tamely ramified supercuspidals, which I've never read, so I'm not sure where this originates. | |
| May 5, 2016 at 18:25 | comment | added | MathStudent | @P.L Can you give me a reference for the fact that if the interwining of $\lambda$ is $J$ then the induced representation is supercuspidal? | |
| May 5, 2016 at 18:02 | history | edited | PL. | CC BY-SA 3.0 |
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| May 5, 2016 at 17:52 | history | answered | PL. | CC BY-SA 3.0 |