branchingRule -- A Lie algebra module viewed as a module over a Lie subalgebra

Usage:

branchingRule(V,S)
Inputs:
- V, an instance of the type LieAlgebraModule,
- S, a string, a list, a matrix, or an instance of the type LieAlgebra,
Outputs:
- V', an instance of the type LieAlgebraModule,

Description

S must be a subset of vertices of the Dynkin diagram of the Lie algebra of V, or a matrix, or a string, see subLieAlgebra; or a sub-Lie algebra. Returns V viewed as a module over the Lie subalgebra determined by S.

i1 : g=simpleLieAlgebra("D",4);

i2 : M=adjointModule g;

i3 : branchingRule(M,{1,2,3})

                                 2
o3 = LL     (𝔞 ) ++ (LL     (𝔞 ))  ++ LL     (𝔞 )
       0,0,0  3        0,1,0  3         1,0,1  3

o3 : LieAlgebraModule over 𝔞
                            3

Ways to use branchingRule:

branchingRule(LieAlgebraModule,LieAlgebra)
branchingRule(LieAlgebraModule,List)
branchingRule(LieAlgebraModule,Matrix)
branchingRule(LieAlgebraModule,String)

For the programmer

The object branchingRule is a method function.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/LieAlgebraRepresentations/documentation.m2:1222:0.