This function implements Freudenthal’s recursive algorithm; see Humphreys, Introduction to Lie Algebras and Representation Theory, Section 22.3. Let V be the irreducible g-module with highest weight v. This function returns a hash table whose keys are the weights appearing in V and whose values are the multiplicities of these weights. The character of V can be easily computed from this information (but characters of Lie algebra modules have not been implemented in this version of LieTypes).
i1 : g=simpleLieAlgebra("A",2)
o1 = g
o1 : LieAlgebra
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i2 : V=irreducibleLieAlgebraModule({2,1},g)
o2 = V
o2 : g module
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i3 : weightDiagram(V)
o3 = HashTable{{-1, -2} => 1}
{-1, 1} => 2
{-2, 0} => 1
{-2, 3} => 1
{-3, 2} => 1
{0, -1} => 2
{0, 2} => 1
{1, -3} => 1
{1, 0} => 2
{2, -2} => 1
{2, 1} => 1
{3, -1} => 1
o3 : HashTable
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