skip to main content

Title: Compact formulas for Macdonald polynomials and quasisymmetric Macdonald polynomials
Authors:
; ; ; ;
Award ID(s):
1953891
Publication Date:
NSF-PAR ID:
10286563
Journal Name:
Proceedings of the 32nd Conference on Formal Power Article Series and Algebraic Combinatorics
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract We provide elementary identities relating the three known types of non-symmetric interpolation Macdonald polynomials. In addition we derive a duality for non-symmetric interpolation Macdonald polynomials. We consider some applications of these results, in particular to binomial formulas involving non-symmetric interpolation Macdonald polynomials.
  2. The Cook-Austral volcanic lineament extends from Macdonald Seamount (east) to Aitutaki Island (west) in the South Pacific Ocean and consists of hotspot-related volcanic islands, seamounts, and atolls. The Cook-Austral volcanic lineament has been characterized as multiple overlapping, age-progressive hotspot tracks generated by at least two mantle plumes, including the Arago and Macdonald plumes, which have fed volcano construction for ~20 m.y. The Arago and Macdonald hotspot tracks are argued to have been active for at least 70 m.y. and to extend northwest of the Cook-Austral volcanic lineament into the Cretaceous-aged Tuvalu-Gilbert and Tokelau Island chains, respectively. Large gaps in samplingmore »exist along the predicted hotspot tracks, complicating efforts seeking to show that the Arago and Macdonald hotspots have been continuous, long-lived sources of hotspot volcanism back into the Cretaceous. We present new major- and trace-element concentrations and radiogenic isotopes for three seamounts (Moki, Malulu, Dino) and one atoll (Rose), and new clinopyroxene 40Ar/39Ar ages for Rose (24.81 ± 1.02 Ma) and Moki (44.53 ± 10.05 Ma). All volcanoes are located in the poorly sampled region between the younger Cook-Austral and the older, Cretaceous portions of the Arago and Macdonald hotspot tracks. Absolute plate motion modeling indicates that the Rose and Moki volcanoes lie on or near the reconstructed traces of the Arago and Macdonald hotspots, respectively, and the 40Ar/39Ar ages for Rose and Moki align with the predicted age progression for the Arago (Rose) and Macdonald (Moki) hotspots, thereby linking the younger Cook-Austral and older Cretaceous portions of the long-lived (>70 m.y.) Arago and Macdonald hotspot tracks.« less