Skew odd orthogonal characters and interpolating Schur polynomials

Abstract We introduce two vertex operators to realize skew odd orthogonal characters and derive the Cauchy identity for the skew characters via the Toeplitz–Hankel‐type determinant as an analog of Schur functions. The method also gives new proofs of the Jacobi–Trudi identity and Gelfand–Tsetlin patterns for . Moreover, combining the vertex operators related to characters of types (Baker, J. Phys. A . 29 (12) (1996), 3099–3117; Jing and Nie, Ann. Combin . 19 (2015), 427–442) and the new vertex operators related to ‐type characters, we obtain three families of symmetric polynomials that interpolate among characters of , , and . Their transition formulae are also explicitly given among symplectic, orthogonal, and odd orthogonal characters.