LieAlgebraModule _ ZZ -- Pick out one irreducible submodule of a Lie algebra module

Operator: _

Description

If a number is given, the ordering is the same as when the module is displayed:

i1 : g=simpleLieAlgebra("A",2);

i2 : (adjointModule g)^**3

               2              4              8              2              6              4                          2
o2 = (LL   (g))  ++ (LL   (g))  ++ (LL   (g))  ++ (LL   (g))  ++ (LL   (g))  ++ (LL   (g))  ++ LL   (g) ++ (LL   (g))
        0,0            0,3            1,1            1,4            2,2            3,0           3,3          4,1

o2 : LieAlgebraModule over g

i3 : oo_2

o3 = LL   (g)
       1,1

o3 : irreducible LieAlgebraModule over g

Instead one can simply use a weight or irreducible module as subscript:

i4 : g=simpleLieAlgebra("A",3);

i5 : M=(adjointModule g)^**2

o5 = M

o5 : LieAlgebraModule over g

i6 : describe M

                                                           2
o6 = LL     (g) ++ LL     (g) ++ LL     (g) ++ (LL     (g))  ++ LL     (g) ++ LL     (g)
       0,0,0         0,1,2         0,2,0          1,0,1           2,0,2         2,1,0

i7 : M_{1,0,1}

o7 = 2

i8 : M_(trivialModule g)

o8 = 1

Ways to use this method:

LieAlgebraModule _ LieAlgebraModule
LieAlgebraModule _ List
LieAlgebraModule _ Vector
LieAlgebraModule _ ZZ -- Pick out one irreducible submodule of a Lie algebra module

The source of this document is in LieTypes.m2:2675:0.