Timeline for Weight diagrams and semi-simple Lie algebras
Current License: CC BY-SA 2.5
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 8, 2011 at 18:12 | comment | added | David Hill | @ARupinski: Of course, you are right! | |
| Apr 8, 2011 at 9:18 | vote | accept | K McKenzie | ||
| Apr 7, 2011 at 22:54 | comment | added | ARupinski | @David: $B_2$ and $C_2$ define the same Lie Algebra. Consequently one usually specifies that the $B_n$ series begins at $n=2$ and the $C_n$-series begins with $n=3$ (although occasionally the reverse is also used) | |
| Apr 7, 2011 at 22:50 | answer | added | ARupinski | timeline score: 1 | |
| Apr 7, 2011 at 21:35 | comment | added | David Hill | Then the answer is no. You cannot differentiate $B_2$ and $C_2$. | |
| Apr 7, 2011 at 19:53 | comment | added | K McKenzie | Thanks! To ARupinski, what I'm asking is whether, given a weight diagram corresponding to an arbitrary representation of an algebra A, that weight diagram is a weight diagram of a representation of the algebra A only (ie, no other algebra). Does that help? To Mariano - thank you so much for the link! Awesome. Can I ask you what section (to your mind) implies that the answer is yes? (My math is a few orders of magnitude beneath these guys [and doubtless you guys].) | |
| Apr 7, 2011 at 19:01 | comment | added | ARupinski | Are you referring to the weight diagram of a given representation, or to the entire weight lattice of the algebra? | |
| Apr 7, 2011 at 18:04 | comment | added | Mariano Suárez-Álvarez | I googled for "weight diagram" and (after a first result which is a link to your question (it is amazing how fast Google indexes MO!) comes a link math.oregonstate.edu/~tevian/JOMA/joma_paper_softlinks.pdf to a paper by Wangberg and Dray which, if I understand correctly, says the answer to your question is yes. | |
| Apr 7, 2011 at 17:46 | history | asked | K McKenzie | CC BY-SA 2.5 |