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Combinatorial models for Quasicrystals and Schur-Weyl Duality
Abstract
Quasicrystals were defined by Cain and Malheiro and Maas-Gariépy to model the decomposition of Schur polynomials into fundamental quasisymmetric functions. We define a new combinatorial model for crystal graphs of type An−1, called parsed content words, for which the decomposition into quasicrystals is particularly evident. We use the model to describe a combinatorial interpretation of Schur-Weyl duality and recover the classical combinatorial proof of the well-known expansion of homogeneous symmetric functions into Schur functions within our framework.
Related
- Combinatorial description of the mirabolic quantum Schur-Weyl duality
- Schur--Weyl duality for coideal subalgebras of quantum affine superalgebras of type A
- Dualities in one-dimensional quantum lattice models: Lie groups, Schur-Weyl duality and symmetry breaking
- Affine quantum Schur--Weyl duality
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BibTeX
@misc{appleby2026combinatorial,
title = {{Combinatorial models for Quasicrystals and Schur-Weyl Duality}},
author = {Glenn Appleby and Mary Claire Simone and Tamsen Whitehead McGinley},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33772},
eprint = {2610.33772},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33772},
}
RIS
TY - UNPB
TI - Combinatorial models for Quasicrystals and Schur-Weyl Duality
AU - Glenn Appleby
AU - Mary Claire Simone
AU - Tamsen Whitehead McGinley
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33772
UR - https://arxiv.org/abs/2610.33772
AB - Quasicrystals were defined by Cain and Malheiro and Maas-Gariépy to model the decomposition of Schur polynomials into fundamental quasisymmetric functions. We define a new combinatorial model for crystal graphs of type A_n−1, called parsed content words, for which the decomposition into quasicrystals is particularly evident. We use the model to describe a combinatorial interpretation of Schur-Weyl duality and recover the classical combinatorial proof of the well-known expansion of homogeneous symmetric functions into Schur functions within our framework.
ER -