Character expansions and affine Jacobi-Trudi identities

Abstract

We provide character expansions of certain specialisations of multiparameter Hall--Littlewood polynomials of types ${\mathrm{B}}_n$, ${\mathrm{C}}_n$, and ${\mathrm{BC}}_n$ for rectangular shapes. We use these expansions to establish the six Jacobi-Trudi-type identities conjectured by Ole Warnaar in 2025.