Timeline for Cauchy identity for Jack functions
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 7, 2023 at 22:54 | vote | accept | Giulio R | ||
| May 3, 2023 at 18:20 | answer | added | Giulio R | timeline score: 5 | |
| May 3, 2023 at 16:39 | comment | added | Jules Lamers | Just to include the answer directly here: the LHS of (2) changes to $\sum_\lambda P^{(\alpha)}_\lambda(x) \, P^{(1/\alpha)}_{\lambda'}(y)$ for Jack (and $\sum_\lambda P_\lambda(x;q,t) \, P_{\lambda'}(y;t,q)$ for Macdonald, both) in the monic '$P$-normalisation; the RHS remains the same. This is consistent as $\alpha=1$ gives Schur. This identity appears to have been found independently by Gaudin and Macdonald. | |
| May 3, 2023 at 14:24 | comment | added | Giulio R | Thanks! Indeed looking for it, I found it here: kurims.kyoto-u.ac.jp/EMIS/journals/SLC/opapers/s28macdonald.pdf (formula 2.6) | |
| May 3, 2023 at 13:15 | comment | added | Sam Hopkins | The second identity you listed is usually called the "dual Cauchy identity." This could help with your searches. | |
| May 3, 2023 at 10:16 | history | asked | Giulio R | CC BY-SA 4.0 |