# 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

${\displaystyle \displaystyle \sigma _{\lambda }=\det(\sigma _{\lambda _{i}+j-i})_{1\leq i,j\leq r}}$

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, MR1464693
• Sottile, Frank (2001) [1994], "Schubert calculus", in Hazewinkel, Michiel (ed.), Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4