Skew Symplectic and Orthogonal Schur Functions

Naihuan Jing ; Zhijun Li ; Danxia Wang

Symmetry, integrability and geometry: methods and applications, Tome 20 (2024)

Résumé

Using the vertex operator representations for symplectic and orthogonal Schur functions, we define two families of symmetric functions and show that they 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.

Détail

Keywords: skew orthogonal/symplectic Schur functions, Jacobi–Trudi identity, Gelfand–Tsetlin patterns, vertex operators.

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