Timeline for Why are parabolic subgroups called "parabolic subgroups"?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| May 18, 2010 at 15:11 | vote | accept | Timothy Chow | ||
| May 17, 2010 at 13:03 | comment | added | Jim Humphreys |
P.S. A late instance of "parabolic" in connection with the modular group occurs in a 1974 thesis at NYU by the last student there of Wilhelm Magnus: Nonparabolic Subgroups of the Modular Group by Carol Tretkoff. But in line with Benoit's answer, the underlying rationale for the usage comes from study of homogeneous spaces such as $G/P$ in Lie theory. Borel himself didn't use the term "parabolic subgroup" in his 1956 Annals paper, but focused on complete/projective varieties starting with $G/B$. By 1962 he as well as Tits and others were using the term in print.
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| May 17, 2010 at 11:25 | comment | added | Jim Humphreys | Borel's attribution of the terminology "parabolic subgroup" to Godement is reasonable, but Timothy Chow's first option probably comes closest to the rationale behind this choice. Study of the modular group by Fricke, Klein, and others distinguished several types of elements: "elliptic", "hyperbolic", "parabolic" (the latter typically coming from unipotent matrices). When Dan Mostow was asked about the origin of the naming convention back in 1977, I recall that he attributed it to the parallel with modular groups and parabolic elements. By 1962 Tits was using the term in his papers. | |
| May 17, 2010 at 10:44 | history | answered | Gjergji Zaimi | CC BY-SA 2.5 |