  We give an elementary proof of the first fundamental theorem of the invariant
theory for the orthosymplectic supergroup by generalising the method of Atiyah,
Bott and Patodi to the supergroup context. We use methods from super-algebraic
geometry to convert invariants of the orthosymplectic supergroup into
invariants of the corresponding general linear supergroup on a different space.
In this way, a super Schur-Weyl-Brauer duality is established between the
orthosymplectic supergroup of superdimension $(m|2n)$ and the Brauer algebra
with parameter $m-2n$. The result may be interpreted in terms of the relevant
Harish-Chandra super pair action (over the complex field), or equivalently, the
orthosymplectic Lie supergroup over the infinite dimensional Grassmann algebra.
We also state a corresponding theorem for the orthosymplectic Lie superalgebra,
which involves an extra invariant generator, the super-Pfaffian.

Representation Theory