97-2 Krasovsky I.V.
A Matrix Commuting with the Square of the Almost Mathieu Operator. (9K, LaTeX) Jan 3, 97
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Abstract. Using a transformation that reduces the almost Mathieu operator to a tridiagonal form with zero main diagonal, a unitary matrix is constructed that commutes with the square of the "$N$-dimensional almost Mathieu" operator $H_\psi$ \begin{eqnarray} (H_{\psi}\psi)_n=\psi_{n-1}+2\cos(\omega n+\theta)\psi_n+\psi_{n+1},\\ n=0,1,\dots,N-1; \psi_{-1}=\psi_{N-1}; \psi_{N}=\psi_{0}; \end{eqnarray} in the case when $\omega=2\pi M/N$ (numbers $M$, $N$ are relatively prime integers), $N$ is divisible by 4, and $\cos(N\theta)=-1$.

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