Timeline for Irreducible Degrees and the Order of a Finite Group
Current License: CC BY-SA 3.0
8 events
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Apr 18, 2013 at 13:58 | history | edited | David E Speyer | CC BY-SA 3.0 |
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| Apr 11, 2013 at 2:58 | comment | added | David E Speyer | Thanks for the reference to the Bump and Ginzburg paper! That's very nice. | |
| Apr 10, 2013 at 23:27 | comment | added | Gene S. Kopp | Another interesting point about the Bump and Ginzburg paper is that it provides a combinatorial interpretation for the $a_g$ assuming the existence of an involution on $G$ with certain properties. | |
| Apr 10, 2013 at 23:24 | comment | added | Gene S. Kopp | Bump and Ginzburg remark on page 4 of their paper "Generalized Frobenius-Schur Numbers" that the Mathieu group $M_{11}$ provide another example where some of the $a_g$ are negative (and that the observation goes back to Solomon and Thompson). @David, your example is smaller (order 1920 versus 7920), so maybe it is not well-known. | |
| Apr 9, 2013 at 2:56 | comment | added | P Vanchinathan | Correction to my earlier comment: I meant real two-dimensional representation for odd cyclic groups. | |
| Apr 8, 2013 at 23:38 | comment | added | P Vanchinathan | @David Speyer: Thanks for the detailed answer here and at SE. I am teaching rep theory without using group algebras and fumbling. In Lagrange's theorem we see cosets are of same cardinality and provide a partition of $G$. About degree of intermediate fields in finite extensions also we have a transparent proof. I am looking for such a simple underlying idea. As odd ordered cyclic groups have 2-dimensional irreps as symmetries of regular polygons we need to bring the dependence on complex numbers (via Schur's lemma). Not that easy perhaps. :-( | |
| Apr 8, 2013 at 14:46 | history | answered | David E Speyer | CC BY-SA 3.0 |