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Fixed points of DT transformations, cluster exponents and degrees of Weyl groups

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arxiv 2503.11391 v3 pith:6UOCYHMW submitted 2025-03-14 math.RA math.RT

Antoine de Saint Germain , Jiang-Hua Lu This is my paper · ORCID
classification math.RAmath.RT
keywords fixedpointstransformationsclusterdegreesexponentsfiniteweyl
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Inspired by a recent work of Y. Mizuno, we show that the DT transformations on a cluster ensemble of finite type admit unique totally positive fixed points, and that the exponents of the linearizations of the DT transformations at the fixed points are precisely the degrees of the Weyl group of the corresponding finite root system.

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  1. 2-periodic frieze patterns

    math.RA 2025-06 conditional novelty 7.0 of 10

    Every 2-periodic positive real mesh frieze of finite type A, D or E is constant, or lies in a one- or two-parameter family, with the exact count depending on the type.

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