Timeline for Reduction formula for Schubert polynomials
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Oct 13, 2015 at 10:20 | vote | accept | Matt Samuel | ||
| Oct 13, 2015 at 2:44 | comment | added | Matt Samuel | @AlexanderWoo Found it, thanks for the tip. | |
| Oct 13, 2015 at 2:39 | answer | added | Matt Samuel | timeline score: 2 | |
| Oct 9, 2015 at 0:52 | comment | added | Matt Samuel | @AlexanderWoo I believe the first formula I quoted is from Billey and Bergeron's paper, so that definitely seems like a reasonable place to look, thanks. | |
| Oct 8, 2015 at 23:37 | comment | added | Alexander Woo | I think this is just the statement that the "coproduct LR coefficients" are (in type A) the same as the "product LR coefficients" (i.e. the usual ones). Geometrically it has something to do with the duality between cohomology and homology, and combinatorially it has something to do with the Hopf algebra structure on quasi-symmetric functions. You might try looking through Nantel Bergeron's papers. | |
| Oct 8, 2015 at 4:16 | history | edited | Matt Samuel |
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| Oct 8, 2015 at 0:48 | comment | added | Matt Samuel | @Suvrit Well, my advisor (Anders Buch) has a paper expressing Schubert polynomials in terms of Schur polynomials, so the determinantal representations of those apply, though I'm not sure that really counts because it's not just one determinant. I haven't heard of a true determinantal formula for Schubert polynomials. | |
| Oct 8, 2015 at 0:45 | comment | added | Suvrit | Thanks for the info Matt! Btw do you know if Schubert polynomials have some nice determinantal representations? | |
| Oct 8, 2015 at 0:31 | comment | added | Matt Samuel | @Suvrit Thanks. After looking at this I remembered what is called a Cauchy formula and one way to prove the identity in my question is using the Cauchy formula for ordinary double Schubert polynomials. The proof is pretty easy, but the proof of the formula in my dissertation was pretty easy too and nevertheless no one saw it before, so, you know. | |
| Oct 8, 2015 at 0:24 | comment | added | Suvrit | Here's the arXiv link: arxiv.org/abs/q-alg/9703047 | |
| Oct 8, 2015 at 0:16 | comment | added | Matt Samuel | @Suvrit Thanks, it's too bad payment is required, I'm no longer affiliated with a university and I really miss having free access to these paid journals. | |
| Oct 8, 2015 at 0:14 | comment | added | Suvrit | Some of the "Cauchy Identities" in link.springer.com/content/pdf/10.1023/… seem relevant (for double quantum Schubert polynomials) --- though this is purely a web search result.. | |
| Oct 7, 2015 at 23:41 | history | asked | Matt Samuel | CC BY-SA 3.0 |