Naqvi, Yusra;
Sahi, Siddhartha;
Sergel, Emily;
(2023)
Interpolation Polynomials, Bar Monomials, and Their Positivity.
International Mathematics Research Notices
, 2023
(8)
pp. 6809-6844.
10.1093/imrn/rnac049.
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Abstract
We prove a conjecture of Knop–Sahi on the positivity of interpolation polynomials, which is an inhomogeneous generalization of Macdonald’s conjecture for Jack polynomials. We also formulate and prove the nonsymmetric version of this conjecture, and in fact, we deduce everything from an even stronger positivity result. This last result concerns certain inhomogeneous analogues of ordinary monomials that we call bar monomials. Their positivity involves in an essential way a new partial order on compositions that we call the bar order, and a new operation that we call a glissade.
| Type: | Article |
|---|---|
| Title: | Interpolation Polynomials, Bar Monomials, and Their Positivity |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1093/imrn/rnac049 |
| Publisher version: | https://doi.org/10.1093/imrn/rnac049 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher's terms and conditions. |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10146890 |
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