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

Partition functions of integrable lattice models and combinatorics of symmetric polynomials