Polynomial KP and BKP $$\tau $$-Functions and Correlators

Lattices of polynomial KP and BKP $\tau$-functions labelled by partitions, with the flow variables equated to finite power sums, as well associated multipair multipoint correlation functions are expressed via generalizations Jacobi's bialternant formula for Schur Nimmo's Pfaffian ratio $Q$-functions. These obtained applying Wick's theorem fermionic vacuum expectation value representations in which infinite group element acting on lattice basis states stabilizes vacuum.