Timeline for Elementary proof of K-saturation conjecture
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 16, 2013 at 7:45 | vote | accept | Per Alexandersson | ||
| Jul 16, 2013 at 7:45 | answer | added | Per Alexandersson | timeline score: 1 | |
| May 6, 2013 at 13:43 | comment | added | Allen Knutson | You're right, I was confusing myself. Anyway perhaps the simplest, or at least best-motivated, proof is that saturation is equivalent to Horn's conjecture (this is a simple, but great, observation of Belkale) and Horn's conjecture has a very natural proof due to Purbhoo and Sottile. | |
| May 6, 2013 at 8:12 | comment | added | Per Alexandersson | Correct me if I'm wrong, but for the non-skew version, $K_{\lambda,w}>0$ iff $\lambda \geq_d w$ in dominance order. And I suppose that $\lambda \geq_d w \Leftrightarrow n\lambda \geq_d nw$ is easy to show... | |
| May 6, 2013 at 3:53 | comment | added | Allen Knutson | Oops, that's supposed to be the $[nw$ weight space$]$. | |
| May 6, 2013 at 3:52 | comment | added | Allen Knutson | To my mind, the elementary reason that saturation might be true for ordinary (not skew) Kostka numbers is that the ring $\oplus_n (V_{n\lambda})[w$ weight space$]$ might be generated in degree $1$. Moreover, that would explain Fulton's conjecture (that if the degree $1$ piece is $1$-d, then so is every piece), which we also proved. But in general this ring is not generated in degree $1$! I forget Fulton's counterexample in which the degree $2$ part is larger than $sym^2$ of the degree $1$ part, or something like that, but there is one. | |
| May 5, 2013 at 16:10 | history | asked | Per Alexandersson | CC BY-SA 3.0 |