Lattice path constructions for orthosymplectic determinantal formulas

Abstract

We give lattice path proofs of determinantal formulas for orthosymplectic characters. We use the spo(2m,n)-tableaux introduced by Benkart, Shader and Ram, which have both a semistandard symplectic part and a row-strict part. We obtain orthosymplectic Jacobi–Trudi identities and an orthosymplectic Giambelli identity by associating spo(2m,n)-tableaux to certain families of nonintersecting lattice paths and using an adaptation of the Gessel–Viennot method.