Geodesic
Semifinite harmonic functions on the zigzag graph
Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 3, pp. 52-74

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We study semifinite harmonic functions on the zigzag graph, which corresponds to the Pieri rule for the fundamental quasisymmetric functions $\{F_{\lambda}\}$. The main problem, which we solve here, is to classify the indecomposable semifinite harmonic functions on this graph. We show that these functions are in a natural bijective correspondence with some combinatorial data, the so-called semifinite zigzag growth models. Furthermore, we describe an explicit construction that produces a semifinite indecomposable harmonic function from every semifinite zigzag growth model. We also establish a semifinite analogue of the Vershik–Kerov ring theorem.
Keywords: fundamental quasisymmetric functions, zigzags, branching graphs, AF-algebras, semifinite traces.
Mots-clés : compositions 
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     author = {N. A. Safonkin},
     title = {Semifinite harmonic functions on the zigzag graph},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {52--74},
     publisher = {mathdoc},
     volume = {56},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2022_56_3_a3/}
}
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N. A. Safonkin. Semifinite harmonic functions on the zigzag graph. Funkcionalʹnyj analiz i ego priloženiâ, Tome 56 (2022) no. 3, pp. 52-74. http://geodesic.mathdoc.fr/item/FAA_2022_56_3_a3/