Timeline for Why complete symmetric polynomials and elementary symmetric polynomials are dual to each other?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 3, 2014 at 23:54 | vote | accept | Bombyx mori | ||
| Jun 1, 2014 at 8:07 | vote | accept | Bombyx mori | ||
| Jun 1, 2014 at 8:07 | |||||
| May 31, 2014 at 23:15 | answer | added | Steven Sam | timeline score: 10 | |
| May 31, 2014 at 13:12 | comment | added | Bombyx mori | @MarkWildon: I managed to find the paper. Give me sometime to read it. | |
| May 31, 2014 at 12:49 | comment | added | Bombyx mori | @MarkWildon: I see. I need some time to digest this as I learned all these formulas from a few days ago. | |
| May 31, 2014 at 12:31 | comment | added | Mark Wildon | All the formulae you give follow easily from the involution (using that it sends $s_\lambda$ to $s_{\lambda^\star}$ where $\lambda^\star$ is the conjugate partition to $\lambda$). There are many combinatorial proofs of the Pieri rules: see e.g. Loehr's article Abacus proofs of Schur function identities. Moving to the symmetric group, $s_\lambda$ is sent to $\chi^\lambda$ and the involution becomes multiplication by the sign character of $S_n$. For me this makes some dual identities more intuitive (especially when they involve plethysm) but it's just a change of language. | |
| May 31, 2014 at 11:55 | history | asked | Bombyx mori | CC BY-SA 3.0 |