Giambelli's formula [SEP] named after
Giambelli's formula
In mathematics, Giambelli's formula, named after Giovanni Giambelli, expresses Schubert classes in terms of special Schubert classes, or Schur functions in terms of complete symmetric functions.
It states
where σ is the Schubert class of a partition λ.
Giambelli's formula is a consequence of Pieri's formula. The Porteous formula is a generalization to morphisms of vector bundles over a variety.
Porteous formula
In mathematics, the Porteous formula, or Thom–Porteous formula, or Giambelli–Thom–Porteous formula, is an expression for the fundamental class of a degeneracy locus (or determinantal variety) of a morphism of vector bundles in terms of Chern classes. Giambelli's formula is roughly the special case when the vector bundles are sums of line bundles over projective space. pointed out that the fundamental class must be a polynomial in the Chern classes and found this polynomial in a few special cases, and found the