8 problems

Let $a$ be a spin taking values modulo $N$, let $\omega$ be an $N$th root of unity, and define the order parameter by … Here $k$ is the universal chiral-Potts-model constant, and…

Baxter's product-form conjecture. For $i=0,\ldots,N-1$ and $r=1,\ldots,N-i$, the functions $G_{p,V^i p}(r)$ have a simple form as a product of ${\cal S}$ functions.

Blockwise intertwining conjecture. Such a relation exists for all sizes of the chain, and for each of the $4L$ blocks in (HKredu2).

Involutive-permutation solution conjecture. The solutions of (HR2) are linear combinations of $4L$ solutions that are involutive permutation matrices $I_n$ in the original basis in…

Let $H$ be a nearest-neighbour Hamiltonian represented in a one-parameter algebraic framework with a derivation whose recursively generated charges are $Q_0:=H$ and…

Let … where … For the polynomial … write $\Lambda_n^P=c_{nN+P}$. Au–Yang–Perk coefficient conjecture. The coefficients are symmetric, $\mathcal G_{\ell,k}=\mathcal G_{k,\ell}$, and…

Let ${\mathcal M}_r$ be the order parameter, let ${\mathcal Z}_Q$ denote the partition function with fixed boundary condition of type $Q$, and define … Here $y_i$, $y'_i$,…

Cyclic complexity conjecture. The algebraic complexity of this cyclic transformation should be the same as that of the corresponding transformation for arbitrary $q\times q$ matric…