next | previous | forward | backward | up | top | index | toc | packages | Macaulay2 website
LieTypes :: multiplicity(List,LieAlgebraModule)

multiplicity(List,LieAlgebraModule) -- compute the multiplicity of a weight in a Lie algebra module

Synopsis

Description

The example below shows that the $sl_3$ module with highest weight $(2,1)$ contains the weight $(-1,1)$ with multiplicity 2.

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

o1 = g

o1 : simple LieAlgebra
i2 : V=irreducibleLieAlgebraModule({2,1},g)

o2 = V

o2 : irreducible LieAlgebraModule over g
i3 : multiplicity({-1,1},V)

o3 = 2

See also

Ways to use this method: