Timeline for Dimensions of irreducible representations of $GL(n,F_q)$ are polynoms in q having roots ONLY at roots of unity and zero?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Aug 16, 2017 at 6:33 | comment | added | Alexander Chervov | Your paper is "on my table". It is wonderful ! | |
| Aug 14, 2017 at 23:05 | comment | added | Jim Humphreys | The nice 2011 Springer text by Cedric Bonnafe does provide a good modern treatment of complex representations of the special linear group SL$_2$, while my older exposition (limited to groups over the prime field but freely available online) is more elementary even though much less up-to-date: maa.org/sites/default/files/pdf/upload_library/22/Ford/… | |
| Aug 14, 2017 at 22:55 | history | edited | Jim Humphreys | CC BY-SA 3.0 |
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| Aug 14, 2017 at 18:41 | comment | added | Alexander Chervov | Yes that is true , however what I observe in literature that even GL case except GL2 is not exposed in some good pedagogical manner... So MO seems best way to ask for help... There are really lots of expositions of GL2.... | |
| Aug 14, 2017 at 18:20 | comment | added | Jim Humphreys | Concerning degrees, this has not been the sole concern: the natural problem is to determine all character values (i.e., the character table). This gets understood so far by a complicated recursive method, which makes it seem at the moment impossible to write degrees in all ranks as polynomials in $q$ with integral (or rational) coefficients except for finite general linear groups. I'm not sure how far one can expect to write down closed degree formulas for all finite groups of Lie type, but Frank Luebeck and others have computed a lot of special cases. | |
| Aug 14, 2017 at 17:51 | comment | added | Alexander Chervov | Thank you for the answer (and my is UPvote). About ' many questions ' my basic question is the first one - the one in the title. | |
| Aug 14, 2017 at 17:00 | history | answered | Jim Humphreys | CC BY-SA 3.0 |