Timeline for Structure of Deligne-Lusztig representations $R_{T,\theta}$ for ministropic $T$ and cuspidal representations
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Oct 12, 2015 at 13:46 | vote | accept | John Binder | ||
| Oct 11, 2015 at 22:50 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
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| Oct 9, 2015 at 23:52 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
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| Oct 8, 2015 at 16:03 | comment | added | John Binder | thanks for your comment. It seems we're on the same page now, and I'm glad I wasn't mistaken about cuspidals only coming from anisotropic tori. | |
| Oct 8, 2015 at 15:19 | comment | added | Jim Humphreys | @John: Having given the set-up some more thought, I've edited my answer so that the tori in question are anisotropic over the finite field. Sorry for the added confusion. It's true that cuspidal irreducible characters can't occur as constituents in ordinary parabolic induction for proper parabolics, but in the D-L construction a generalized character coming from an anisotropic (or minisotropic) torus may well have a mixture of irreducibles as constituents including both cuspidal and non-cuspidal characters. | |
| Oct 8, 2015 at 15:13 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
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| Oct 8, 2015 at 14:34 | comment | added | Jim Humphreys | @John: Maybe it's best to include a definition of "minisotropic" in your question? And what would it mean for $R_{T,\theta}$ to be "cuspidal"? | |
| Oct 8, 2015 at 14:28 | comment | added | John Binder | thanks for your answer. I've edited the first line to reflect your note on terminology. Re your second point, perhaps I'm mistaken in the following line of reasoning: let $S\leq T$ be the maximal split component and let $A$ be the maximal split component in the center. If $S \supsetneq A$, then $C_G(S)$ is a Levi component $M$ of a proper parabolic subgroup $P$ of $G$, and we have $T \leq M$. Then any $R_{T,\theta}$ is a character induced from a character $\rho$ on $M$, and thus not cuspidal. It's possible there's an error in my understanding. | |
| Oct 8, 2015 at 14:15 | history | answered | Jim Humphreys | CC BY-SA 3.0 |