Timeline for What is Extreme/Extremal vector according to some weights
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Apr 17, 2010 at 21:33 | vote | accept | Shizhuo Zhang | ||
| Apr 17, 2010 at 13:34 | comment | added | Jim Humphreys | References? Besides textbooks, it's interesting to look at some of the relevant literature such as MR943925 (89j:17009) 17B10 (22E46) Kumar, Shrawan (6-TIFR), Proof of the Parthasarathy-Ranga Rao-Varadarajan conjecture. Invent. Math. 93 (1988), no. 1, 117–130. | |
| Apr 17, 2010 at 13:21 | comment | added | Jim Humphreys | Yes, this is the standard notion developed originally in the setting of finite dimensional irreducible representations of complex semisimple Lie algebras (or groups); extremal weights have multiplicity 1. This can to some extent be carried over to "integrable" representations of affine Kac-Moody algebras, where Kac found a good analogue of the Weyl character formula. Also, the theory of Demazure modules (geometrically motivated) involves study of the subspace obtained by fixing an extremal weight space and applying to it all negative root vectors in the Lie algebra. | |
| Apr 17, 2010 at 13:06 | history | answered | Ben Webster♦ | CC BY-SA 2.5 |