标题： KP乘对关联函数在BKP关联函数中的双线性展开 显示英文标题

标题： Bilinear expansions of KP multipair correlators in BKP correlators

摘要： 在早期的工作中，KP 和 BKP $\tau$-函数的 Schur 格点，分别记为 $\pi_{\lambda}(g) ({\bf t})$和 $\kappa_{\alpha} (h)({\bf t}_B)$，定义为费米子真空期望值，与每个 GL$(\infty)$群元素 $\hat{g}$和 SO$(\tilde{\mathcal{H}}^\pm, Q_\pm)$群元素 $\hat{h}$相关联。 这些格的元素分别由分拆$\lambda$和严格分拆$\alpha$标记。 已经展示了前者可以表示为后者乘积上的有限双线性和。 在本工作中，我们表明，对应于任何给定的$\hat{g}$的双侧 KP Tau 函数也可以表示为相应双侧 BKP Tau 函数的双线性组合。 显示英文摘要

摘要： In earlier work, Schur lattices of KP and BKP $\tau$-functions, denoted $\pi_{\lambda}(g) ({\bf t})$ and $\kappa_{\alpha} (h)({\bf t}_B)$, respectively, defined as fermionic vacuum expectation values, were associated to every GL$(\infty)$ group element $\hat{g}$ and SO$(\tilde{\mathcal{H}}^\pm, Q_\pm)$ group element $\hat{h}$. The elements of these lattices are labelled by partitions $\lambda$ and strict partitions $\alpha$, respectively. It was shown how the former may be expressed as finite bilinear sums over products of the latter. In this work, we show that two-sided KP tau functions corresponding to any given $\hat{g}$ may similarly be expressed as bilinear combinations of the corresponding two-sided BKP tau functions.