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.
Integrable deformations of CFTs and the discrete Hirota equations
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abstract
We solve the discrete Hirota equations (Kirillov-Reshetikhin Q-systems) for $A_r$, and their analogue for $D_r$, for the cases where the second variable ranges over either a finite set or over all integers. Until now only special solutions were known. We find all solutions for which no component vanishes, as required in the known applications. As an introduction we present the known solution where the second variable ranges over the natural numbers.
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2-periodic frieze patterns
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.