  The matrix model of topological field theory for the moduli space of p-th
spin curves is extended to the case of the Lie algebra of the orthogonal group.
We derive a new duality relation for the expectation values of characteristic
polynomials in the antisymmetric Gaussian matrix model with an external matrix
source. The intersection numbers for non-orientable surfaces of spin curves
with k marked points are obtained from the Fourier transform of the k-point
correlation functions at the critical point where the gap is closing.
