4 problems

Let $\mathfrak{g}$ be the Lie algebra generated by the raising and lowering operators of the periodic Fredkin chain with $N$ sites. Let $\mathrm{S}^z$ be the third component of the…

Let $\mathfrak{g}$ be the Lie algebra generated by the raising and lowering operators $\Sigma^\pm$ of the periodic Fredkin chain with $N$ sites, and set $n=\lceil N/2\rceil$. B- an…

Anti-adjoint representation conjecture. There exist coefficients $\gamma_k$ such that

Let $\Sigma^\pm$ be the raising and lowering operators for the periodic Fredkin chain, let $C$ be the cyclic shift operator, and let $\mathrm{H}$ be its Hamiltonian. An eigenstate…