Calculating entries of unitary 𝑆𝐿𝟹-friezes

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

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OriginalspracheEnglisch
FachzeitschriftJournal of Combinatorial Algebra
Frühes Online-Datum11 März 2025
PublikationsstatusElektronisch veröffentlicht (E-Pub) - 11 März 2025

Abstract

In this article we consider tame $ SL_3 $-friezes that arise by specializing a cluster of Pl\"ucker variables in the coordinate ring of the Grassmannian $ \mathscr{G}(3,n) $ to $ 1 $. We show how to calculate arbitrary entries of such friezes from the cluster in question. Let $ \mathscr{F} $ be such a cluster. We study the set $ \mathscr{F}_x $ of cluster variables in $ \mathscr{F} $ that share a given index $ x $ and derive a structure Theorem for $ \mathscr{F}_x $. These sets prove central to calculating the first and last non-trivial rows of the frieze. After that, simple recursive formulas can be used to calculate all remaining entries.

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Calculating entries of unitary 𝑆𝐿𝟹-friezes. / Surmann, Lucas.
in: Journal of Combinatorial Algebra, 11.03.2025.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

Surmann L. Calculating entries of unitary 𝑆𝐿𝟹-friezes. Journal of Combinatorial Algebra. 2025 Mär 11. Epub 2025 Mär 11. doi: 10.4171/JCA/111, 10.48550/arXiv.2404.09811
Surmann, Lucas. / Calculating entries of unitary 𝑆𝐿𝟹-friezes. in: Journal of Combinatorial Algebra. 2025.
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