Timeline for Equality of codimension under Lusztig-Spaltenstein induction
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Apr 5, 2016 at 2:18 | comment | added | Cheng-Chiang Tsai | Just corrected a mistake which I shamefully didn't understand until today. It's essential to have $H^{\vee}\subset G^{\vee}$ instead of $H\subset G$. For example, if $G=\mathrm{Sp}_4$, then the minimal orbit of $G$ will correspond to the non-trivial local system on the subregular orbit of $G^{\vee}\cong\mathrm{SO}_5$, which is not what I wanted. | |
| Apr 5, 2016 at 2:15 | history | edited | Cheng-Chiang Tsai | CC BY-SA 3.0 |
Correct a fundamental mistake
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| Oct 19, 2015 at 1:14 | vote | accept | Cheng-Chiang Tsai | ||
| Oct 18, 2015 at 17:08 | comment | added | Jim Humphreys | @Tsai: As Jay points out (and Lusztig suggests), there are relevant details in Lusztig's papers. The extra groups $H$ are called "pseudo-Levi subgroups" by his former student Eric Sommers, though Eric and I disagree about whether that label should include the genuine Levi subgroups of parabolic subgroups. | |
| Oct 18, 2015 at 16:01 | answer | added | Jay Taylor | timeline score: 4 | |
| Oct 18, 2015 at 15:17 | history | edited | Cheng-Chiang Tsai | CC BY-SA 3.0 |
added 754 characters in body
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| Oct 9, 2015 at 17:03 | comment | added | Cheng-Chiang Tsai | I learned from Prof. Lusztig that this is (essentially) true, and really follows from that in the definition of $j$-induction, the minimum number $e$ so that the interested rep'n of the Weyl group appears in $\mathrm{Sym}^e(std)$ is the same as the dimension for the Springer fiber. I'll try to add reference later when I read them better. | |
| Oct 7, 2015 at 3:25 | comment | added | Cheng-Chiang Tsai | Definitely! I think their construction showed that the assertion is true when $H$ is a Levi (e.g. via the theorem you pointed out). | |
| Oct 7, 2015 at 3:08 | history | edited | Cheng-Chiang Tsai | CC BY-SA 3.0 |
added 3 characters in body
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| Oct 7, 2015 at 2:04 | comment | added | wky | Theorem 1.3(b) of Lusztig-Spaltenstein (Induced unipotent class) says the springer fiber of $u$ in $G$ has the same dimension as that of $u_H$ in $H$ if $H$ is a Levi of $G$. Is it going to help? | |
| Oct 7, 2015 at 1:50 | comment | added | Allen Knutson | I don't think you want to call the highest root $\rho$ (except in $SL_3$) because that's standardly used for half the sum of the positive roots. | |
| Oct 6, 2015 at 19:13 | history | asked | Cheng-Chiang Tsai | CC BY-SA 3.0 |