Lattice path constructions for orthosymplectic determinantal formulas

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 rowstrict part. We obtain orthosymplectic Jacob-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.