Timeline for Expanding the zonal polynomial $Z_\lambda(x/(1-x))$
Current License: CC BY-SA 4.0
12 events
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| Jun 2, 2021 at 15:31 | history | edited | Marcel | CC BY-SA 4.0 |
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| May 24, 2021 at 18:09 | comment | added | user35313 | @PerAlexandersson : The Schur function case is handled generally in arxiv.org/pdf/1601.01581.pdf. Look at corollary 3.5. These are special cases of canonical stable Grothendieck polynomials. | |
| May 24, 2021 at 16:08 | history | edited | Marcel | CC BY-SA 4.0 |
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| May 21, 2021 at 19:31 | comment | added | Per Alexandersson | Ah interesting. The coefficients in your formula, they have been studied before, see sciencedirect.com/science/article/pii/0001870885901215 (Binomial determinants, paths, and hook length formulae, by I. Gessel) | |
| May 21, 2021 at 16:58 | comment | added | Marcel | @PerAlexandersson Thanks. For Schur functions I have done it in the appendix to this paper: arxiv.org/abs/2008.07419 | |
| May 21, 2021 at 16:52 | comment | added | Per Alexandersson | The one who I would ask is Valentin Feray. By the way, do you have a reference for the statement regarding the Schur functions? | |
| May 21, 2021 at 16:07 | comment | added | Marcel | @PerAlexandersson Yes, that possibility has occurred to me. It is doable, but quite messy. For Schur functions there is a more direct approach, using a scalar product. I was hoping something like that could also work for zonals. | |
| May 21, 2021 at 15:51 | comment | added | Per Alexandersson | So, there are power-sum expansions of the Jack polynomials known, and on these, your substitution is easy. However, expanding this back into Jack (or Zonal, for the case alpha=2) seems hard | |
| May 21, 2021 at 13:31 | comment | added | Marcel | @PerAlexandersson I mean $Z_\lambda(\frac{x_1}{1-x_1}, \frac{x_2}{1-x_2},\cdots,\frac{x_n}{1-x_n})$ | |
| May 21, 2021 at 13:19 | comment | added | Per Alexandersson | Wait, what is meant by $x/(1-x)$? Do you mean the plethystic substitution which evaluates the Schur in $y,y^2,y^3,\dotsc$ for all variables? | |
| May 21, 2021 at 12:56 | history | edited | Marcel | CC BY-SA 4.0 |
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| May 20, 2021 at 14:10 | history | asked | Marcel | CC BY-SA 4.0 |