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

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

where σ_λ 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