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• W2223584687 endingPage "053111" @default.
• W2223584687 startingPage "053111" @default.
• W2223584687 abstract "The nineteen-vertex model on a periodic lattice with an anti-diagonal twist is investigated. Its inhomogeneous transfer matrix is shown to have a simple eigenvalue, with the corresponding eigenstate displaying intriguing combinatorial features. Similar results were previously found for the same model with a diagonal twist. The eigenstate for the anti-diagonal twist is explicitly constructed using the quantum separation of variables technique. A number of sum rules and special components are computed and expressed in terms of Kuperberg's determinants for partition functions of the inhomogeneous six-vertex model. The computations of some components of the special eigenstate for the diagonal twist are also presented. In the homogeneous limit, the special eigenstates become eigenvectors of the Hamiltonians of the integrable spin-one XXZ chain with twisted boundary conditions. Their sum rules and special components for both twists are expressed in terms of generating functions arising in the weighted enumeration of various symmetry classes of alternating sign matrices (ASMs). These include half-turn symmetric ASMs, quarter-turn symmetric ASMs, vertically symmetric ASMs, vertically and horizontally perverse ASMs and double U-turn ASMs. As side results, new determinant and pfaffian formulas for the weighted enumeration of various symmetry classes of alternating sign matrices are obtained." @default.
• W2223584687 created "2016-06-24" @default.
• W2223584687 creator A5001760680 @default.
• W2223584687 creator A5045890146 @default.
• W2223584687 date "2016-05-26" @default.
• W2223584687 modified "2023-09-27" @default.
• W2223584687 title "Symmetry classes of alternating sign matrices in a nineteen-vertex model" @default.
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• W2223584687 doi "https://doi.org/10.1088/1742-5468/2016/05/053111" @default.
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