Partition functions of integrable lattice models and combinatorics of symmetric polynomials

Abstract

We review and present new studies on the relation between the partition functions of integrable lattice models and symmetric polynomials, and its combinatorial representation theory based on the correspondence, including our work. In particular, we examine the correspondence between the wavefunctions of the XXZ type, Felderhof type and the boson type integrable models and symmetric polynomials such as the Schur, Grothendieck and symplectic Schur functions. We also give a brief report of our work on generalizing the correspondence between the Felderhof models and factorial Schur and symplectic Schur functions.

21 pages, submitted to RIMS Kokyuroku Bessatsu

References in corpus (3)

• Quantum integrable combinatorics of Schur polynomials
• Refined Cauchy/Littlewood identities and six-vertex model partition functions: II. Proofs and new conjectures
• Tokuyama's Identity for Factorial Schur Functions

Cited by in corpus (3)

• Dual wavefunction of the Felderhof model
• Combinatorial properties of symmetric polynomials from integrable vertex models in finite lattice
• Quantum inverse scattering method and generalizations of symplectic Schur functions and Whittaker functions