FUNCTION: CgMultiplicity - calculate weight multiplicities

CALLING SEQUENCE:

CgMultiplicity(typ, lambda, mu)

CG[CgMultiplicity](typ, lambda, mu)

PARAMETERS:

typ = one of the classical group A, B, C or D

lambda, mu = any lists denoting partitions

SYNOPSIS:

• The CgMultiplicity function calculates the multiplicity K(lambda, mu) of the weight mu in the irreducible module (of the simple Lie algebra of type typ) with highest weight lambda, using the Freudenthal formula.

• For type A, K(lambda, mu) is the corresponding Kostka number.

• Whenever there is a conflict between the function name CgMultiplicity and another name used in the same session,use the long form CG['CgMultiplicity'].

EXAMPLES:

> with(CG):
> CgMultiplicity(A, [9,1], [5,3,2]);
 
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