Special polynomials related to the supersymmetric eight-vertex model: a summary. (English) Zbl 1330.82014
The author introduces and studies symmetric polynomials, which as very special cases include polynomials related to the supersymmetric eight-vertex model, and other elliptic models with \(\Delta=\pm 1/2\). It is shown that up to a change of variables, these polynomials satisfy a Schrödinger equation with elliptic potential and that specializations of the polynomials are tau functions for Painlevé VI.
Reviewer: Nasir N. Ganikhodjaev (Kuantan)
MSC:
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 35Q40 | PDEs in connection with quantum mechanics |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
| 05E05 | Symmetric functions and generalizations |
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