A Ratio of Alternants Formula for Loop Schur Functions
Combinatorics
2018-05-18 v2
Abstract
Lam and Pylyavskyy introduced loop symmetric functions as a generalization of symmetric functions. They defined loop Schur functions as generating functions over semistandard tableaux with respect to a `colored weight,' and they proved a Jacobi--Trudi-style determinantal formula for these generating functions. We prove that loop Schur functions can be expressed as a ratio of `loop alternants,' extending the analogy with Schur functions. As an application, we give a new proof of the loop version of the Murnaghan--Nakayama rule.
Keywords
Cite
@article{arxiv.1504.03782,
title = {A Ratio of Alternants Formula for Loop Schur Functions},
author = {Gabriel Frieden},
journal= {arXiv preprint arXiv:1504.03782},
year = {2018}
}
Comments
12 pages. (v2) Added a denominator formula (Corollary 3.2) and an alternative ratio of alternants formula (Theorem 3.3); improved the exposition; changed notational conventions for $h_k^{(r)}$ and alternants