Timeline for On existence of a certain irreducible character of $SL(5, q)$
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
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| S Nov 28, 2016 at 17:13 | history | bounty ended | user97635 | ||
| S Nov 28, 2016 at 17:13 | history | notice removed | user97635 | ||
| Nov 28, 2016 at 11:55 | vote | accept | user97635 | ||
| Nov 28, 2016 at 11:00 | answer | added | Frank Lübeck | timeline score: 10 | |
| S Nov 27, 2016 at 16:53 | history | bounty started | user97635 | ||
| S Nov 27, 2016 at 16:53 | history | notice added | user97635 | Canonical answer required | |
| Nov 26, 2016 at 15:18 | comment | added | user97635 | @JimHumphreys Thanks for the link. I know that the main theme of Malle's paper is investigating groups of Lie type in non-defining characteristics. I just meant that in "Sec 2.1" he has settled the general framework of Lusztig's Jordan decomposition. I tried to follow Digne and Michel's book in the basic formulations. Also, the assumption $p>5$ is a guess, so it's okay to work on larger $q$. The main problem is to find a semisimple element of $PGL(5,q)$ with desired centralizer (If there exists any)... | |
| Nov 26, 2016 at 15:05 | comment | added | Jim Humphreys | P.S. Here is a link to Malle's paper: ams.org/journals/ert/2007-11-09/S1088-4165-07-00312-3 | |
| Nov 26, 2016 at 15:00 | comment | added | Jim Humphreys | Thanks for the added comments, but I'm still confused about your basic formulation. Though Luebeck's computations of the character tables are limited to groups of rank $<9$, he does indicate that his degree polynomials are "generic" and I guess should be valid for larger $q$: math.rwth-aachen.de/~Frank.Luebeck/chev/DegMult/… In any case, I find your final paragraph hard to follow, but I'll try again. | |
| Nov 26, 2016 at 10:12 | history | edited | user97635 | CC BY-SA 3.0 |
the google book's link of the relevant page of Digne and Michel's book added
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| Nov 26, 2016 at 9:49 | comment | added | user97635 | @JimHumphreys I added some more description to clarify my question. By the way, you can also take a look at Section 2.1 of Gunter Malle's paper "Height 0 characters of finite groups of Lie type, Represent. Theory (2007)" for a short review of Lusztig's parametrization of characters for an arbitrary connected reductive group. | |
| Nov 26, 2016 at 9:31 | history | edited | user97635 | CC BY-SA 3.0 |
according to Jim's comment, more descriptions were added to clarify the question.
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| Nov 26, 2016 at 9:26 | history | edited | user97635 | CC BY-SA 3.0 |
according to Jim's comment, more descriptions were added to clarify the question.
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| Nov 26, 2016 at 8:18 | comment | added | user97635 | @JimHumphreys I think Lusztig's Jordan decomposition of irreducible characters has been generalized also to connected reductive groups with disconnected center in Lusztig's paper "On the representations of reductive groups with disconnected center" Asterisque 168. Unfortunately, I don't have access to the original paper, but this have been covered in standard texts such as Theorem 13.23 and Remark 13.24 of Digne and Michel's book, or more clearly in Theorem 1.73 and Corollary 1.74 of Jay Taylor's thesis tel.archives-ouvertes.fr/tel-00709051/document. | |
| Nov 25, 2016 at 23:12 | comment | added | Jim Humphreys | I'm confused about the formulation here. Lusztig's theory based on the Deligne-Lusztig construction allows one to compute (in principle) all the character degrees. However, what Carter calls a "Jordan decomposition" of characters assumes that the ambient algebraic group has a connected center. This is not true for special linear groups but is true for general linear groups. Can you clarify what you are asking for, preferably with reference to Lusztig's papers? | |
| Nov 25, 2016 at 17:50 | comment | added | user97635 | @StefanKohl Not yet. First I wanted to be sure about the correctness of my arguments. | |
| Nov 25, 2016 at 17:48 | comment | added | Stefan Kohl♦ | Have you asked Frank Lübeck already? | |
| Nov 25, 2016 at 16:52 | history | edited | user97635 | CC BY-SA 3.0 |
A link added
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| Nov 25, 2016 at 16:46 | history | asked | user97635 | CC BY-SA 3.0 |