Timeline for Weight multiplicities for some particular representations of SO(2m).
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 25, 2017 at 16:33 | vote | accept | emiliocba | ||
| Mar 9, 2017 at 10:39 | answer | added | emiliocba | timeline score: 2 | |
| Sep 4, 2014 at 7:37 | comment | added | emiliocba | I considered $p<m$ only because the case $p=m$ splits ($\Lambda_{k,m}$ and $(k+1)\varepsilon_1+ \varepsilon_2 +\dots+ \varepsilon_{m-1} - \varepsilon_m$), so I didn't want to explain these technicalities. | |
| Sep 3, 2014 at 20:25 | comment | added | Jim Humphreys | I'm not optimistic about finding closed formulas for all weight multiplicities in these cases. In general, Freudenthal's formula is probably best for direct computations when other methods are inadequate. (By the way, it's unclear to me why you specify $p < m$ rather than $p \leq m$. Maybe I'm misunderstanding your notation.) | |
| Sep 3, 2014 at 17:32 | answer | added | Peter Crooks | timeline score: 0 | |
| Sep 3, 2014 at 14:07 | comment | added | emiliocba | @Vít: you are right, the formula is expressed in terms of other coefficients. I hope there exists a more explicit closed formula, since these representations are very particular. | |
| Sep 3, 2014 at 12:27 | comment | added | Vít Tuček | A quick google search discovered an article by Koike, that expresses all you want in terms of Littlewood-Richardson adn Kostka coefficients. sciencedirect.com/science/article/pii/0021869387901001 | |
| Sep 3, 2014 at 10:11 | history | asked | emiliocba | CC BY-SA 3.0 |