Character expansions and affine Jacobi-Trudi identities

Source 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.