Quantum integrable combinatorics of Schur polynomials

Abstract

We examine and present new combinatorics for the Schur polynomials from the viewpoint of quantum integrability. We introduce and analyze an integrable six-vertex model which can be viewed as a certain degeneration model from a t-deformed boson model. By a detailed analysis of the wavefunction from the quantum inverse scattering method, we present a novel combinatorial formula which expresses the Schur polynomials by using an additional parameter, which is in the same sense but different from the Tokuyama formula. We also give an algebraic analytic proof for the Cauchy identity and make applications of the domain wall boundary partition functions to the enumeration of alternating sign matrices.

27 pages

References in corpus (6)

• Refined Cauchy and Littlewood identities, plane partitions and symmetry classes of alternating sign matrices
• An Izergin-Korepin procedure for calculating scalar products in six-vertex models
• The 6-vertex model and deformations of the Weyl character formula
• Doubly-refined enumeration of Alternating Sign Matrices and determinants of 2-staircase Schur functions
• $L^p$ solutions of BSDEs with a new kind of non-Lipschitz coefficients
• Half-turn symmetric alternating sign matrices and Tokuyama type factorisation for orthogonal group characters

Cited by in corpus (2)

• Combinatorial properties of symmetric polynomials from integrable vertex models in finite lattice
• Partition functions of integrable lattice models and combinatorics of symmetric polynomials