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# 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 /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/LieAlgebraRepresentations/documentation.m2:1326:0.