6 problems

For a positive integer $N$, let $X_j^{(N)}(z)$, for $j=0,\dots,N$, be the tetrahedral $X$-operators depending on the spectral parameter $z$. Commutativity conjecture. For an arbitr…

Let $i$ and $n$ be positive integers, let $z_j$ be variables, let $\mathcal{D}_j$ be the operators appearing in the modified Schubert-polynomial formalism, and let $\partial_j$ den…

Let $R$ be an operator identity of degree $3$ and multiplicity $1$ on an associative triple system. Let $v\in\mathbb{F}^4$ be the coefficient vector of $R$, and suppose that $v$ pr…

Let $P$, $Q$, and $V$ be as in Lem.. The octagon equation of the non-compact quantum dilogarithm. … This identity is presented as the equation corresponding to Fock–Goncharov's…

Let $P$, $Q$, and $V$ be as in Lem.. The hexagon equation of the non-compact quantum dilogarithm. … This identity is presented as the equation corresponding to Fock–Goncharov's…

Let $P$, $Q$, and $V$ be as in Lemma cited in the source. The octagon equation. … This identity is the operator relation corresponding to Fock–Goncharov's $G_2$-type identity; the…