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

中文翻译：

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多项式KP和BKP $$ \ tau $$τ-函数和相关器

多项式KP和BKP \（\ tau \） -用分区标记的函数的格子，其流量变量等于有限幂和，以及相关的多对KP和多点BKP相关函数，通过针对Schur的Jacobi双替换公式的概括来表示函数和Schur Q函数的Nimmo Pfaffian比公式。这些是通过将维克定理应用于费米离子真空期望值表示形式而得到的，其中作用在基态晶格上的无穷大元素稳定了真空。