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Eigenvectors of open Bazhanov-Stroganov quantum chain. (English) Zbl 1105.82007
The Bazhanov-Stroganov quantum chain is considered, which can be reformulated as Baxter’s inverse SOS model, and covers the chiral Potts model and the relativistic Toda chain. Using an iterative procedure, adding one particle at a time, it is shown how eigenvectors and eigenvalues of the generating polynomial $$A_n(\lambda)$$, the upper left entry of the monodromy matrix, can be obtained. The result is given using a special function attached to the Fermat curve $$x^N+y^N=1$$, a root of unity analogue of the $$\Gamma_q$$-function.

##### MSC:
 82B23 Exactly solvable models; Bethe ansatz 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 81R12 Groups and algebras in quantum theory and relations with integrable systems 82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics
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