PreprintCC BY 4.0arXiv
Rook characters as symmetric functions
Abstract
We give several characterizations of an inhomogeneous basis of the ring of symmetric functions whose evaluations are the character values of the irreducible representations of the rook monoid (symmetric inverse semigroup). Using Schur--Weyl duality, we show that the transition coefficients of this basis with the power symmetric basis are the characters of the propagating partition algebra (dual symmetric inverse monoid algebra). In addition, the structure coefficients of this basis are equal to the coefficients in the smash (or Heisenberg) product of Schur functions.
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BibTeX
@misc{orellana2026rook,
title = {{Rook characters as symmetric functions}},
author = {Rosa Orellana and Alexander N. Wilson and Mike Zabrocki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09042},
eprint = {2609.09042},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09042},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Rook characters as symmetric functions
AU - Rosa Orellana
AU - Alexander N. Wilson
AU - Mike Zabrocki
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09042
UR - https://arxiv.org/abs/2609.09042
AB - We give several characterizations of an inhomogeneous basis of the ring of symmetric functions whose evaluations are the character values of the irreducible representations of the rook monoid (symmetric inverse semigroup). Using Schur--Weyl duality, we show that the transition coefficients of this basis with the power symmetric basis are the characters of the propagating partition algebra (dual symmetric inverse monoid algebra). In addition, the structure coefficients of this basis are equal to the coefficients in the smash (or Heisenberg) product of Schur functions.
ER -