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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

\( \displaystyle \sigma_\lambda= \det(\sigma_{\lambda_i+j-i})_{1\le i,j\le r} \)

where σλ 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.


References

Fulton, William (1997), Young tableaux, London Mathematical Society Student Texts 35, Cambridge University Press, ISBN 978-0-521-56144-0, ISBN 978-0-521-56724-4, MR 1464693
Sottile, Frank (2001), "Schubert calculus", in Hazewinkel, Michiel, Encyclopedia of Mathematics, Springer, ISBN 978-1-55608-010-4

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