Symmetric functions and wavefunctions of the six-vertex model by Izergin-Korepin analysis

Abstract

We analyze wavefunctions of the six-vertex model by extending the Izergin-Korepin analysis on the domain wall boundary partition functions. We particularly focus on the case with triangular boundary. By using the $U_q(s{l}_2)$ $R$-matrix and a special class of the triangular $K$-matrix, we first introduce an analogue of the wavefunctions of the integrable six-vertex model with triangular boundary. We first give a characterization of the wavefunctions by extending our recent work of the Izergin-Korepin analysis of the domain wall boundary partition function with triangular boundary, and then determine the explicit form of the symmetric functions representing the wavefunctions by showing that it satisfies all the required properties. We also illustrate the Izergin-Korepin analysis for the case of ordinary wavefunctions as it is the basic case.

v2, 31 pages, 14 figures, contents enlarged and title changed. arXiv admin note: text overlap with arXiv:1703.06250

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• Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions
• A class of partition functions associated with $E_{\tau ,\eta }(g{l}_3)$ by Izergin-Korepin analysis
• Higher rank elliptic partition functions and multisymmetric elliptic functions
• A duality formula between elliptic determinants
• Elliptic free-fermion model with OS boundary and elliptic Pfaffians
• Integrable models and $K$-theoretic pushforward of Grothendieck classes