Timeline for Representation of GL(n, F_p) over F_p, for n small
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Dec 10, 2014 at 20:52 | comment | added | H. Gao | @Jim. Yes, I know of that book, and will read it. Thanks again! | |
| Dec 10, 2014 at 19:08 | comment | added | Jim Humphreys | @Gao: I wrote a fairly detailed survey Modular Representations of Finite Groups of Lie Type, which appeared in 2006 as London Math. Soc. Lecture Note Ser. 326 (Cambridge U. Press). Almost nothing there is original, but it includes some treatment of special cases including general linear groups. You might find the 460 references useful. (See also the revisions on my homepage.) | |
| Dec 9, 2014 at 18:13 | comment | added | Jim Humphreys | P.S. For small ranks and small primes, you should look at Luebeck's computations: math.rwth-aachen.de/~Frank.Luebeck/chev/WMSmall/index.html For $SL_4$ with $p > 4$ see $\S7$ in Jantzen's paper in Math. Z. 140 (1974) and his Durham conference article in English in Finite Simple Groups II (Academic Press, 1980). For $GL_n$ you just have to multiply by powers of det, which requires mainly some bookkeeping. | |
| Dec 9, 2014 at 18:10 | comment | added | H. Gao | @ Jim, Thank you very much for all the references! | |
| Dec 9, 2014 at 14:30 | comment | added | Jim Humphreys | To clarify terminology: the definition of "Weyl module" has been dualized in Jantzen's book Representations of Algebraic Groups, which Geordie refers to. (See my notes people.math.umass.edu/~jeh/pub/weyl.pdf) This makes no difference for the composition factors. The case $n=2$ goes back to classical work of Brauer-Nesbitt, while $n=3$ was done (modulo Steinberg's 1963 paper) by a student of Curtis in his 1966 thesis, and $n=4$ is due to Jantzen in 1974 for $p>n$ (the Coxeter number). For "small" $p$ lots of uncertainties remain, but computers help a bit. | |
| Dec 9, 2014 at 10:13 | answer | added | Geordie Williamson | timeline score: 5 | |
| Dec 9, 2014 at 1:18 | review | First posts | |||
| Dec 9, 2014 at 1:22 | |||||
| Dec 9, 2014 at 1:15 | history | asked | H. Gao | CC BY-SA 3.0 |