Schur Function Identities Arising From the Basic Representation of A2(2)

A Lie theoretic interpretation is given for some formulas of Schur functions and Schur Q -functions. Two realizations of the basic representation of the Lie algebra A 2 ( 2 ) are considered; one is on the fermionic Fock space and the other is on the bosonic polynomial space. Via the boson–fermion correspondence, simple relations of the vacuum expectation values of fermions turn out to be algebraic relations of Schur functions.