11 problems

A rational integrable quantum field theory is understood to have a factorized S-matrix. Functional-identity conjecture. Similar functional identities for the Rogers dilogarithm sho…

A functional identity of the dilogarithm is an equality involving dilogarithms whose arguments are rational functions. Wojtkowiak's result, as summarized in the source, states that…

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…

Let an exchange graph be the graph whose vertices are seeds of a cluster algebra and whose edges correspond to mutations. Its fundamental group consists of homotopy classes of clos…

Let $A$ be the inverse Cartan matrix of one of the $ADET$ series of simple Lie algebras, and consider Bethe ansatz equations … A dilogarithm identity is an identity associated with…

Let a non-trivial rational conformal field theory have effective central charge, and let the Rogers dilogarithm be denoted by $\operatorname{L}$. The relevant dilogarithm identitie…

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…