Commutation and normal ordering for operators on symmetric functions
Combinatorics
2020-04-14 v4
Abstract
We study the commutation relations and normal ordering between families of operators on symmetric functions. These operators can be naturally defined by the operations of multiplication, Kronecker product, and their adjoints. As applications we give a new proof of the skew Littlewood-Richardson rule and prove an identity about the Kronecker product with a skew Schur function.
Cite
@article{arxiv.1509.02581,
title = {Commutation and normal ordering for operators on symmetric functions},
author = {Emmanuel Briand and Peter R. W. McNamara and Rosa Orellana and Mercedes Rosas},
journal= {arXiv preprint arXiv:1509.02581},
year = {2020}
}
Comments
24 pages, 5 figures. Comments welcome. Dedicated to Ira Gessel on the occasion of his retirement. This new version includes some new results, some additional explanations, and fixes a few typos