This CGC generator computes SU(N) Clebsch-Gordan coefficients (CGCs)
for the decomposition of the direct product S x S' of two irreps into
a direct sum of irreps S'',
using a program written by Arne Alex (click to download C++ source code),
based on an algorithm exploiting Gelfand-Tsetlin calculus described here
[equation numbers given below in square brackets refer to this link].

Conventions

S = irrep label [Eq. (19)]: a sequence of N nonincreasing, nonnegative integers, the last one being 0, e.g. S = (2 2 0) for SU(3)

dim(S) = dimension of irrep S [Eq. (22)]

P(S) = irrep index [Eq. (C2)]: assigns to each irrep S a unique nonnegative integer

M = state label [Eq. (20)]: a Gelfand-Tsetlin pattern,
e.g. the highest-weight state of S=(2 2 0) has the form M =

2

2

0

2

2

2

Q(M) = state index [Eq. (C7)]: assigns to each state of irrep S a unique integer between 1 and dim(S)

alpha = outer multiplicity index [Eq. (2)]: a positive integer that distinguishes different occurences of the same irrep S'' in the decomposition of S x S'

The CGCs that express a state |M''> from irrep S'' (with outer multiplicity index alpha)
as a linear combination of states |M> and |M'> from irreps S and S', respectively,
are defined by the formula [Eq. (5)]:

Tasks performed by the CGC-generator (1-4: decomposition of SxS'; 5-10: properties of SU(N) irreps):