Timeline for Decomposition of GL(2,p) into irreducible representations
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
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| Aug 14, 2012 at 19:59 | comment | added | Alexander Chervov | nice question ! | |
| Jul 9, 2010 at 5:41 | vote | accept | Klim Efremenko | ||
| Jul 8, 2010 at 17:31 | history | edited | Victor Protsak | CC BY-SA 2.5 |
\otimes --> \times
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| Jul 8, 2010 at 17:23 | answer | added | Victor Protsak | timeline score: 3 | |
| Jul 6, 2010 at 6:10 | vote | accept | Klim Efremenko | ||
| Jul 7, 2010 at 11:46 | |||||
| Jul 5, 2010 at 13:14 | answer | added | David E Speyer | timeline score: 8 | |
| Jul 5, 2010 at 10:38 | comment | added | bavajee | Another nice source for the computation of the character table is in Etingof's lectures on representation theory: www-math.mit.edu/~etingof/cltrunc.pdf | |
| Jul 5, 2010 at 10:20 | history | edited | Wadim Zudilin | CC BY-SA 2.5 |
typos fixed
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| Jul 5, 2010 at 9:44 | comment | added | Qiaochu Yuan | What I've got so far: there are two obvious copies of the trivial representation: one coming from the fact that G fixes the origin, and the other coming from the fact that G fixes the sum over all points besides the origin. There is also a subrepresentation spanned by sums over all the points contained in each line through the origin; the action of G on this subrepresentation factors through PSL(2, p), and since the action of PSL(2, p) on the projective line is doubly transitive this subrepresentation is irreducible. | |
| Jul 5, 2010 at 8:53 | comment | added | Robin Chapman | To find the representations all you need is the characters. Each character $\chi$ has a corresponding central idempotent $e_\chi$ in the group algebra. Hitting your representation with $e_\chi$ will give the sum of all irreps with character $\chi$ inside it. | |
| Jul 5, 2010 at 8:22 | comment | added | Klim Efremenko | Acctually I want to know how $C^X$ decomposed and not just what irreducible represintations it contain, i.e. I want to know not only irreducible sub-repesintation in $C^X$ but also homomorphism from it to C^X. | |
| Jul 5, 2010 at 6:39 | comment | added | Robin Chapman | I don't know the answer, but the character table for $G$ can be found in various texts, for instance the third edition of Lang's Algebra. The character of the permutation representation on $X$ is easy to compute. Using the orthogonality relations one gets the decomposition of the permutation character into irreducibles. With a little more work, one can get the decomposition on the level of actual representations. | |
| Jul 5, 2010 at 6:34 | history | asked | Klim Efremenko | CC BY-SA 2.5 |