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

· 2025 · math.RA · arXiv 2503.11391

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abstract

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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2-periodic frieze patterns

math.RA · 2025-06-30 · conditional · novelty 7.0

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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  • 2-periodic frieze patterns math.RA · 2025-06-30 · conditional · none · ref 4 · internal anchor

    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.