Monk's formula
Encyclopedia
In mathematics, Monk's formula, found by , is an analogue of Pieri's formula
that describes the product of a linear Schubert polynomial
by a Schubert polynomial. Equivalently, it describes the product of a special Schubert cycle by a Schubert cycle in the cohomology
of a flag manifold
.
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....
that describes the product of a linear Schubert polynomial
Schubert polynomial
In mathematics, Schubert polynomials are generalizations of Schur polynomials that represent cohomology classes of Schubert cycles in flag varieties.They were introduced by and are named after Hermann Schubert.-Background:...
by a Schubert polynomial. Equivalently, it describes the product of a special Schubert cycle by a Schubert cycle in the cohomology
Cohomology
In mathematics, specifically in algebraic topology, cohomology is a general term for a sequence of abelian groups defined from a co-chain complex. That is, cohomology is defined as the abstract study of cochains, cocycles, and coboundaries...
of a flag manifold
Flag manifold
In mathematics, a generalized flag variety is a homogeneous space whose points are flags in a finite-dimensional vector space V over a field F. When F is the real or complex numbers, a generalized flag variety is a smooth or complex manifold, called a real or complex flag manifold...
.