Lett Math Phys (2017) 107:1235–1263
Dual wavefunction of the Felderhof model
Received: 1 July 2016 / Revised: 5 December 2016 / Accepted: 29 December 2016 /
Published online: 24 January 2017
© Springer Science+Business Media Dordrecht 2017
Abstract We study the Felderhof free-fermion six-vertex model, whose wavefunction
recently turned out to possess rich combinatorial structure of the Schur polynomials.
We investigate the dual version of the wavefunction in this paper, which seems to be a
harder object to analyze. We evaluate the dual wavefunction in two ways. First, we give
the exact correspondence between the dual wavefunction and the Schur polynomials,
for which two proofs are given. Next, we make a microscopic analysis and express
the dual wavefunction in terms of strict Gelfand–Tsetlin pattern. As a consequence
of these two ways of evaluation of the dual wavefunction, we obtain a dual version
of the Tokuyama combinatorial formula for the Schur polynomials. We also give a
generalization of the correspondence between the dual wavefunction of the Felderhof
model and the factorial Schur polynomials.
Keywords Integrable lattice models · Yang–Baxter equation · Symmetric polynomi-
als · Combinatorial representation theory
Mathematics Subject Classiﬁcation 05E05 · 05E10 · 16T25 · 16T30 · 17B37
Integrable lattice models [1–4] in mathematical physics have played important roles
in the developments of algebras, combinatorics and representation theory. One of the
most fundamental models in integrable lattice models is the six-vertex models [5,6].
Faculty of Marine Technology, Tokyo University of Marine Science and Technology, Etchujima
2-1-6, Koto-Ku, Tokyo 135-8533, Japan