Timeline for Young tableaux for exceptional Lie algebras
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 26, 2018 at 14:29 | comment | added | Gro-Tsen | @SamHopkins Ah yes, thank you, I often get them backwards. | |
| Jun 26, 2018 at 13:20 | comment | added | Sam Hopkins | @Gro-Tsen: it's Young diagrams which index irreducible representations. Young Tableaux can be used e.g. to give a basis of the corresponding irreducible representation (since the number of tableaux of a given shape is equal to the dimension of the representation). | |
| Jun 26, 2018 at 11:53 | vote | accept | Nadia SUSY | ||
| Jun 26, 2018 at 8:07 | comment | added | Gro-Tsen | Maybe it's worth pointing out the "well known": irreducible representations of any semisimple Lie algebra are labeled by their highest weight, which can be expressed by the (nonnegative integer) coefficients of the latter on the basis of the fundamental weights. This is what Young tableaux do (the coefficients being the differences between lengths of successive lines, or something). So if you just want to label representations, the classical highest weight theory is all you need. If you want to branch or compute tensor products, of course, you need a more sophisticated theory. | |
| Jun 26, 2018 at 6:58 | answer | added | Zurab Silagadze | timeline score: 4 | |
| Jun 25, 2018 at 21:00 | comment | added | Sam Hopkins | These slides seem like a nice introduction to the Littelmann path model theory, and explain the connection with tableaux as well: people.bath.ac.uk/lpah20/GeomSemNP.pdf | |
| Jun 25, 2018 at 13:56 | comment | added | Sam Hopkins | I am not an expert but I think the "Littelmann path model" is something sort of like what you are asking about: en.wikipedia.org/wiki/Littelmann_path_model | |
| Jun 25, 2018 at 13:54 | history | asked | Nadia SUSY | CC BY-SA 4.0 |