6 problems

Zamolodchikov–Ravanini–Tateo–Valleriani conjecture. The solution is periodic with

Let $X$ be a simply-laced connected Dynkin diagram of finite type with rank $r$, Coxeter number $h=h(X)$, and vertex set $I=1,\dots,r1$. Let $\ell\geq 2$ and let…

Tateo's dilogarithm identities.

Let $X_r$ and $X'_{r'}$ be simply laced Dynkin diagrams of finite type, with index sets $I$ and $I'$, ranks $r$ and $r'$, and Coxeter numbers $h$ and $h'$. Let $Y_{ii'}(u)$ be a po…

Let $X_r$ and $X'_{r'}$ be simply laced Dynkin diagrams of finite type, with index sets $I$ and $I'$, Coxeter numbers $h$ and $h'$, and ranks $r$ and $r'$. A family of positive rea…

Let $X_r$ be a simply laced Dynkin diagram of finite type with rank $r$ and index set $I$, and let $ell a \geq 2$ be an integer. Let $L(x)$ be the Rogers dilogarithm function. For p…