English

Semifinite harmonic functions on the zigzag graph

Representation Theory 2022-05-10 v3 Combinatorics Operator Algebras

Abstract

We study semifinite harmonic functions on the zigzag graph, which corresponds to Pieri's rule for the fundamental quasisymmetric functions {Fλ}\{F_{\lambda}\}. The main problem, which we solve here, is to classify the indecomposable semifinite harmonic functions on this graph. We describe the set of classification parameters and an explicit construction that produces a semifinite indecomposable harmonic function out of every point of this set. We also establish a semifinite analog of the Vershik-Kerov ring theorem.

Keywords

Cite

@article{arxiv.2110.01508,
  title  = {Semifinite harmonic functions on the zigzag graph},
  author = {Nikita Safonkin},
  journal= {arXiv preprint arXiv:2110.01508},
  year   = {2022}
}
R2 v1 2026-06-24T06:36:36.382Z