Calculating entries of unitary $SL_3$-friezes

Research output: Working paper/Preprint › Preprint

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Original languageEnglish
Publication statusE-pub ahead of print - 15 Apr 2024

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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    math.CO, 13F60, 14M15, 05C99, 05E99, 51M20

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Calculating entries of unitary $SL_3$-friezes. / Surmann, Lucas.
2024.

Research output: Working paper/Preprint › Preprint

Surmann, L. (2024). Calculating entries of unitary $SL_3$-friezes. Advance online publication.
Surmann L. Calculating entries of unitary $SL_3$-friezes. 2024 Apr 15. Epub 2024 Apr 15.
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