A Determinantal Formula for Orthosymplectic Schur Functions

We prove a new determinantal formula for the characters of irreducible representations of orthosymplectic Lie superalgebras analogous to the formula developed by Moens and Jeugt (J Algebraic Combin 17(3):283–307, 2003) for general linear Lie superalgebras. Our proof uses the Jacobi–Trudi type formulas for orthosymplectic characters. As a consequence, we show that the odd symplectic characters introduced by Proctor (Invent Math 92(2):307–332, 1988) are the same as the orthosymplectic characters with some specialized indeterminates. We also give a generalization of an odd symplectic character identity due to Brent, Krattenthaler and Warnaar (J Combin Theory Ser A 144:80–138, 2016).