lieType -- outputs the Lie type of a generalized flag variety

Synopsis

Usage:

lieType X
Inputs:
- X, a GKM variety,
Outputs:
- a string, of the form "A", "B", "C" or "D"

Description

If $X$ is a generalized flag variety or a generalized Schubert variety constructed using the method generalizedFlagVariety or generalizedSchubertVariety, this method outputs the Lie type of $X$.

i1 : X = generalizedFlagVariety("A",3,{2}); -- The Grassmannian Gr(2,4)

i2 : Y = generalizedFlagVariety("B",2,{1}); -- The Orthogonal Grassmannian SOGr(1,5)

i3 : lieType(X)

o3 = A

i4 : lieType(Y)

o4 = B

If the GKM variety is not a generalized flag variety or a generalized Schubert variety, prints error.

Caveat

The method projectiveSpace dose not cache the Lie type.

Ways to use `lieType` :

"lieType(GKMVariety)"

For the programmer

The object lieType is a method function.