FlMatchingField -- the class of matching fields for partial flag varieties

Description

Common ways to define flag matching fields:

flMatchingField-- defined in terms of tuples or a weight matrix
diagonalMatchingField-- the diagonal matching field
matchingFieldFromPermutation-- family of matching fields indexed by permutations

Technical details. A flag matching field is derived from the class HashTable. All flag matching fields have the following fields:

kList of type ZZ
n of type ZZ
grMatchingFieldList of type List, the list of Grassmannian matching fields contained within, accessible with the functiongetGrMatchingFields
cache

Everything else, including: weight matrices; polynomial rings, maps and ideals; polyhedra such as the weight matrix cone and matching field polytope, are all stored inside the cache. Note that the package does not export the keys, such as kList or n. If you wish to directly address the contents of the FlMatchingField, then use "debug MatchingFields".

Functions and methods returning an object of class FlMatchingField :

flMatchingField -- Construct a matching field for a partial flag variety

Methods that use an object of class FlMatchingField :

FlMatchingField == FlMatchingField -- equality of flag matching fields
getGrMatchingFields(FlMatchingField) -- see getGrMatchingFields -- The Grassmannian matching fields of a Flag matching field
getTuples(FlMatchingField) -- see getTuples -- The tuples of a matching field
getWeightMatrix(FlMatchingField) -- see getWeightMatrix -- weight matrix that induces the matching field
getWeightPluecker(FlMatchingField) -- see getWeightPluecker -- weight of the Pluecker variables induced by the weight matrix
isCoherent(FlMatchingField) -- see isCoherent -- Is the matching field coherent
isToricDegeneration(FlMatchingField) -- see isToricDegeneration -- Does the matching field give rise to a toric degeneration
matchingFieldIdeal(FlMatchingField) -- see matchingFieldIdeal -- The toric ideal of a matching field
matchingFieldPolytope(FlMatchingField) -- see matchingFieldPolytope -- The polytope of a matching field
matchingFieldRingMap(FlMatchingField) -- see matchingFieldRingMap -- monomial map of the matching field
net(FlMatchingField) -- see net(GrMatchingField) -- display a matching field
NOBody(FlMatchingField) -- see NOBody -- Newton-Okounkov body of the matching field
plueckerAlgebra(FlMatchingField) -- see plueckerAlgebra -- Pluecker algebra of a (partial) flag variety
plueckerIdeal(FlMatchingField) -- see plueckerIdeal -- The Pluecker ideal of a matching field
plueckerMap(FlMatchingField) -- see plueckerMap -- The ring map of the Pluecker embedding
weightMatrixCone(FlMatchingField) -- see weightMatrixCone -- The cone of weight matrices that induce the matching field

For the programmer

The object FlMatchingField is a type, with ancestor classes HashTable < Thing.

FlMatchingField -- the class of matching fields for partial flag varieties

Description

See also

Functions and methods returning an object of class FlMatchingField :

Methods that use an object of class FlMatchingField :

For the programmer

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