论文标题
第九变体偏斜舒尔函数和Q-功能的确定性和PFAFFIAN身份
Determinantal and Pfaffian identities for ninth variation skew Schur functions and Q-functions
论文作者
论文摘要
最近，冈田定义了代数第九个变化偏斜Q-函数，并同时与麦克唐纳的第九个变化偏斜schur函数并行。在这里，我们介绍了这些第九个变化偏斜的偏斜的tableaux定义，并通过非接口晶格路径模型证明了pfaffian外部分解的形式，其形式是Hamel的Pfaffian Pfaffian外部分解身份的第九个变体版本。作为推论，我们得出了Pfaffian的身份，从而推广了Josefiak-Pragacz，Nimmo和最近的冈田。作为此的序言，我们基于（未缩放的）Semistard Tableaux提出了平行的开发，该开发导致Hamel和Goulden的外部分解决定性确定身份的第九个变体版本。在这种情况下，我们提供的推论包括确定性身份，概括了Jacobi-Trudi，Giambelli，Lascoux-Pragacz，Stembridge和Okada的Schur和Skew Schur功能身份。
Recently Okada defined algebraically ninth variation skew Q-functions, in parallel to Macdonald's ninth variation skew Schur functions. Here we introduce a skew shifted tableaux definition of these ninth variation skew Q-functions, and prove by means of a non-intersecting lattice path model a Pfaffian outside decomposition result in the form of a ninth variation version of Hamel's Pfaffian outside decomposition identity. As corollaries to this we derive Pfaffian identities generalizing those of Josefiak-Pragacz, Nimmo, and most recently Okada. As a preamble to this we present a parallel development based on (unshifted) semistandard tableaux that leads to a ninth variation version of the outside decomposition determinantal identity of Hamel and Goulden. In this case the corollaries we offer include determinantal identities generalizing the Schur and skew Schur function identities of Jacobi-Trudi, Giambelli, Lascoux-Pragacz, Stembridge, and Okada.
