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The Lecture Notes in Mathematics number 1689, "Schubert Varieties and Degeneracy Loci" by Fulton and Pragacz seems to be exactly what your you're looking for. I think chapter 6 is particularly relevant.

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The Lecture Notes in Mathematics number 1689, "Schubert Varieties and Degeneracy Loci" by Fulton and Pragacz seems to be exactly what your looking for. I think chapter 6 is particularly relevant.