论文标题
kp $τ$ - 功能的双线性扩展在bkp $τ$ - functions中：一种费米金方法
Bilinear expansions of lattices of KP $τ$-functions in BKP $τ$-functions: a fermionic approach
论文作者
论文摘要
我们得出双线性扩展，表达了由分区标记的kp $τ$插件的晶格的元素，作为一对bkp $τ$功能相关晶格的成对元素的总和，并由严格的分区标记。这概括了早期的结果，该结果将偏斜对称矩阵的未成年人的决定因素和PFAFFIAN，以及用于Schur功能和Schur $ Q $ functions的应用。它是使用KP和BKP $τ$ functions的表示，分别是带电和中性类型的费米子操作员的真空期望值（VEV）。该晶格是通过插入成对的成对创建和歼灭操作员的产品而产生的。结果是将产品扩展为中性费米子发电机中的单个单元的总和，并在相互通勤的亚代伯拉群岛中对操作员产品的VEV进行分解定理。应用程序包括KP和BKP类型的不均匀多项式$τ$ - 功能的情况。
We derive a bilinear expansion expressing elements of a lattice of KP $τ$-functions, labelled by partitions, as a sum over products of pairs of elements of an associated lattice of BKP $τ$-functions, labelled by strict partitions. This generalizes earlier results relating determinants and Pfaffians of minors of skew symmetric matrices, with applications to Schur functions and Schur $Q$-functions. It is deduced using the representations of KP and BKP $τ$-functions as vacuum expectation values (VEV's) of products of fermionic operators of charged and neutral type, respectively. The lattice is generated by insertion of products of pairs of charged creation and annihilation operators. The result follows from expanding the product as a sum of monomials in the neutral fermionic generators and applying a factorization theorem for VEV's of products of operators in the mutually commuting subalgebras. Applications include the case of inhomogeneous polynomial $τ$-functions of KP and BKP type.
