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
λ is the Schubert class of a
partition
Partition may refer to:
Computing Hardware
* Disk partitioning, the division of a hard disk drive
* Memory partition, a subdivision of a computer's memory, usually for use by a single job
Software
* Partition (database), the division of a ...
λ.
Giambelli's formula is a consequence of
Pieri's formula In mathematics, Pieri's formula, named after Mario Pieri, describes the product of a Schubert cycle by a special Schubert cycle in the Schubert calculus, or the product of a Schur polynomial by a complete symmetric function.
In terms of Schur func ...
. The
Porteous formula is a generalization to morphisms of vector bundles over a variety.
See also
*
Schubert calculus
In mathematics, Schubert calculus is a branch of algebraic geometry introduced in the nineteenth century by Hermann Schubert, in order to solve various counting problems of projective geometry (part of enumerative geometry). It was a precursor of ...
- includes examples
References
*
*
Symmetric functions
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