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J-ascent sets in parabolic quotients of Coxeter groups
Abstract
Let (W,S) be a Coxeter system and let J⊆ S. The right J-ascent set ARJ(w)={s∈ S| ws∈JW, ℓ(ws)=ℓ(w)+1} is a natural refinement of the classical ascent set adapted to the parabolic quotient JW. We establish a local transition formula describing the behaviour of J-ascent sets under right multiplication by a simple reflection. As a consequence, for every w∈JW and every s∈ ARJ(w), we prove that ||ARJ(w)|−|ARJ(ws)|| ≤ max{1,deg(s)−1}.
Related
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BibTeX
@misc{chapelierlaget2026jascent,
title = {{$J$-ascent sets in parabolic quotients of Coxeter groups}},
author = {Nathan Chapelier-Laget},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.08465},
eprint = {2609.08465},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.08465},
}
RIS
TY - UNPB
TI - J-ascent sets in parabolic quotients of Coxeter groups
AU - Nathan Chapelier-Laget
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.08465
UR - https://arxiv.org/abs/2609.08465
AB - Let (W,S) be a Coxeter system and let J⊆ S. The right J-ascent set A_R^J(w)={s∈ S| ws∈^JW, ℓ(ws)=ℓ(w)+1} is a natural refinement of the classical ascent set adapted to the parabolic quotient ^JW. We establish a local transition formula describing the behaviour of J-ascent sets under right multiplication by a simple reflection. As a consequence, for every w∈^JW and every s∈ A_R^J(w), we prove that ||A_R^J(w)|−|A_R^J(ws)|| ≤ max{1,deg(s)−1}.
ER -