Hall-Littlewood Expansions of Schur Delta Operators at t=0
Séminaire lotharingien de combinatoire, Tome 79 (2018-2023)
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For any Schur function sν, the associated delta operator Δ'sν is a linear operator on the ring of symmetric functions which has the modified Macdonald polynomials as an eigenbasis. When ν = (1n-1) is a column of length n-1, the symmetric function Δ'en-1en appears in the Shuffle Theorem of Carlsson and Mellit. More generally, when ν = (1k-1) is any column the polynomial Δ'ek-1en is the symmetric function side of the Delta Conjecture of Haglund, Remmel, and Wilson. We give an expansion of ωΔ'sνen at t=0 in the dual Hall-Littlewood basis for any partition ν. The Delta Conjecture at t=0 was recently proven by Garsia, Haglund, Remmel, and Yoo; our methods give a new proof of this result. We give an algebraic interpretation of ωΔ'sνen at t=0 in terms of a Hom-space.
@article{SLC_2018-2023_79_a2,
author = {James Haglund and Brendon Rhoades and Mark Shimozono},
title = {Hall-Littlewood {Expansions} of {Schur} {Delta} {Operators} at t=0},
journal = {S\'eminaire lotharingien de combinatoire},
publisher = {mathdoc},
volume = {79},
year = {2018-2023},
url = {http://geodesic.mathdoc.fr/item/SLC_2018-2023_79_a2/}
}
TY - JOUR AU - James Haglund AU - Brendon Rhoades AU - Mark Shimozono TI - Hall-Littlewood Expansions of Schur Delta Operators at t=0 JO - Séminaire lotharingien de combinatoire PY - 2018-2023 VL - 79 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SLC_2018-2023_79_a2/ ID - SLC_2018-2023_79_a2 ER -
James Haglund; Brendon Rhoades; Mark Shimozono. Hall-Littlewood Expansions of Schur Delta Operators at t=0. Séminaire lotharingien de combinatoire, Tome 79 (2018-2023). http://geodesic.mathdoc.fr/item/SLC_2018-2023_79_a2/