Dual wavefunction of the symplectic ice

Abstract

The wavefunction of the free-fermion six-vertex model was found to give a natural realization of the Tokuyama combinatorial formula for the Schur polynomials by Bump-Brubaker-Friedberg. Recently, we studied the correspondence between the dual version of the wavefunction and the Schur polynomials, which gave rise to another combinatorial formula. In this paper, we extend the analysis to the reflecting boundary condition, and show the exact correspondence between the dual wavefunction and the symplectic Schur functions. This gives a dual version of the integrable model realization of the symplectic Schur functions by Ivanov. We also generalize to the correspondence between the wavefunction, the dual wavefunction of the six-vertex model and the factorial symplectic Schur functions by the inhomogeneous generalization of the model.Comment: 31 pages, 12 figure

Izergin-Korepin Analysis on the Projected Wavefunctions of the Generalized Free-Fermion Model

“…There is also an application to the correlation functions in [18]). This observation triggered studies on finding various generalizations and variations of the Tokuyama-type formula for symmetric functions [19][20][21][22][23][24][25][26][27] such as the factorial Schur functions and symplectic Schur functions, and an interesting notion was introduced furthermore which the number theorists call it the metaplectic ice.…”

Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions

“…Now we state the correspondence between the type I wavefunctions and the generalized symplectic Schur functions. The correspondences (4.18) and (4.19) are generalizations of the one by Ivanov in [43,44] and one of the authors in [67]. One way to prove these correspondences is to adopt the argument by Bump-Brubaker-Friedberg [11] which they viewed the wavefunctions of the freefermionic six-vertex model without reflecting boundary as polynomials in t and studied its properties to find the exact correspondence with the Schur functions.…”

Elliptic supersymmetric integrable model and multivariable elliptic functions

“…It is also interesting to extend the study of partition functions of the elliptic Deguchi-Martin model to other boundary conditions. For example, if one changes the boundary condition of the free-fermionic model to the reflecting boundary condition, other types of symmetric functions such as the symplectic Schur functions [30,31,38] appear. Therefore, one can expect that elliptic analogues of the symplectic Schur functions appear by generalizing the models from trigonometric to elliptic ones.…”

“…Tokuyama formula is a one-parameter deformation of the Weyl character formula for the Schur functions. This fundamental result lead people to find generalizations and variations of the Tokuyama-type formula for various types of symmetric functions [30,31,32,33,34,35,36,37,38]. The latest topic is the introduction of the notion of the metaplectic ice, which is explicitly constructed in [36] by twisting the higher rank Perk-Schultz model.…”