9 problems

Let $\boldsymbol{\mathbf T(u)}$ be the commuting XYZ transfer matrices, let $\boldsymbol{\Psi}$ be the ground-state eigenvector, and let $\boldsymbol{\lambda}$ be its transfer-matr…

Let $\boldsymbol{\boldsymbol{\textit{\Psi}}}$ be the ground-state eigenvector of the supersymmetric XYZ Hamiltonian in the natural normalization, let $\boldsymbol{s_n(z)}$ be the p…

Let $N$ be odd, define $D_N=(N^2-1)/8$, and set … Let $S_1(\alpha)$ be the sum of the components of the normalized ground-state vector and let $\Psi_{-\cdots-}(\alpha)$ be its all-…

Sum-rule divisibility conjecture. If $N=4m-1$ or $N=4m+1$, then

Let $N$ be odd, let $D_N=(N^2-1)/8$, and normalize $|\Psi(\alpha)\rangle$ so that … Let $A_{\mathrm V}(r)$ be the number of vertically symmetric alternating-sign matrices of order…

Let $N=2n+1$ be odd, let $|\Psi(\alpha)\rangle$ be the normalized XYZ ground-state vector, and let $D_N$ be the degree in $\alpha$ of its all-down component…

Let $N$ be odd, and let $|\Psi(\alpha)\rangle$ and $|\bar\Psi(\alpha)\rangle$ be the two parity-sector ground-state vectors of the XYZ Hamiltonian $\mathcal H(\alpha)$. Let…

Let $N$ be odd, set $\alpha=k\operatorname{sn}^2(2\eta)$, and define the XYZ Hamiltonian $\mathcal H(\alpha)$ by … with energy scale $J_x+J_y=2$. XYZ-chain ground-state conjecture.…

Let $N$ be the length of the XYZ spin chain, and let the vector under consideration be the eigenvector associated with Baxter's simple solution of the inversion relations. Baxter's…