Timeline for Algebraic geometry used "externally" (in problems without obvious algebraic structure).
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 24, 2010 at 14:06 | comment | added | Qiaochu Yuan | My understanding is that combinatorial proofs are only known in some special cases, e.g. in type A where one of the permutations avoids some pattern. I'm not sure if positivity is even known in general in the non-crystallographic case. | |
| Jun 24, 2010 at 1:46 | comment | added | CFZ | Haiman's proof of the n! conjecture using the Hilbert scheme is another application to combinatorics. For the K-L coefficients, the first proofs were by intersection cohomology (Beilinson-Bernstein in the early 1980's), but haven't combinatorial proofs been given since that time? | |
| Jun 24, 2010 at 0:06 | comment | added | Alexander Woo | Possibly less lame positivity example(s): Kazhdan-Lusztig polynomials are positive, and the product of Kazhdan-Lusztig basis elements (in the Hecke algebra) expands positively as a sum of Kazhdan-Lusztig basis elements. | |
| Jun 23, 2010 at 22:36 | history | answered | Allen Knutson | CC BY-SA 2.5 |