论文标题
偏斜符号和正交Schur函数
Skew Symplectic and Orthogonal Schur Functions
论文作者
论文摘要
使用顶点操作员表示符号和正交SCHUR函数，我们定义了两个对称函数的家族，并表明它们是Koike和Terada隐含地定义的偏斜符号和偏斜正交Schur多项式，并满足整体分支规则。此外，我们为这些对称函数得出了Jacobi-Trudi身份和Gelfand-Tsetlin模式。此外，顶点操作员方法产生了其cauchy型身份。这表明，顶点操作员表示不仅是研究对称函数的工具，而且还为A，C和D型提供了统一的实现。
Using the vertex operator representations for symplectic and orthogonal Schur functions, we define two families of symmetric functions and show thatthey are the skew symplectic and skew orthogonal Schur polynomials defined implicitly by Koike and Terada and satisfy the general branching rules. Furthermore, we derive the Jacobi-Trudi identities and Gelfand-Tsetlin patterns for these symmetric functions. Additionally, the vertex operator method yields their Cauchy-type identities. This demonstrates that vertex operator representations serve not only as a tool for studying symmetric functions but also offers unified realizations for skew Schur functions of types A, C, and D.
