PreprintCC BY 4.0arXiv
Changing parameters in Hall-Littlewood functions
Abstract
We study the transition coefficients bλ,μ(q,t) of the Hall--Littlewood P-functions Pλ(t) expanded in the basis Pμ(q). We find a tableaux formula when λ is a hook shape which generalizes term-by-term Lascoux-Schutzenberger's charge formula as well as Macdonald's monomial expansion formula for Hall-Littlewood functions. We conjecture that bλ,μ(t+1,t)∈ℤ≥0[t] and prove it when λ is a hook shape, when λ has two-columns and some more simple cases. We prove that bλ,μ(t+n,n)∈ℤ≥0[t] for every n∈ℤ≥0, extending work of Alexandersson, and we record a stability property and some reduction principles.
Related
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BibTeX
@misc{bhattacharya2026changing,
title = {{Changing parameters in Hall-Littlewood functions}},
author = {Aritra Bhattacharya and Ziyi Dai and Qilin Hou and Edward Tong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.41155},
eprint = {2610.41155},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.41155},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Changing parameters in Hall-Littlewood functions
AU - Aritra Bhattacharya
AU - Ziyi Dai
AU - Qilin Hou
AU - Edward Tong
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2610.41155
UR - https://arxiv.org/abs/2610.41155
AB - We study the transition coefficients b_λ,μ(q,t) of the Hall--Littlewood P-functions P_λ(t) expanded in the basis P_μ(q). We find a tableaux formula when λ is a hook shape which generalizes term-by-term Lascoux-Schutzenberger's charge formula as well as Macdonald's monomial expansion formula for Hall-Littlewood functions. We conjecture that b_λ,μ(t+1,t)∈ℤ_≥0[t] and prove it when λ is a hook shape, when λ has two-columns and some more simple cases. We prove that b_λ,μ(t+n,n)∈ℤ_≥0[t] for every n∈ℤ_≥0, extending work of Alexandersson, and we record a stability property and some reduction principles.
ER -