SU(N) Clebsch-Gordan coefficients

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

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)]:

definition of CGCs

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

  1. Find complete set of CGCs arising in decomposition of S x S'
  2. Find all irreps S'' occuring in decomposition of S x S'
  3. Find CGCs for coupling S and S' to S''
  4. Find outer multiplicity of S'' in decomposition of S x S'
  5. Generate list of first n irreps of SU(N)
  6. Generate list of all states M of irrep S
  7. Find index P(S) and dimension dim(S) of irrep S
  8. Find which irrep S is indexed by P
  9. Find index Q(M) of state M in irrep S
  10. Find which state M is indexed by Q in irrep S

1. Find complete set of CGCs arising in decomposition of S x S'

S =

S' =

2. Find all irreps S'' occuring in decomposition of S x S'

S =

S' =

3. Find outer multiplicity of S'' in decomposition of S x S'

S =

S' =

S'' =

4. Find CGCs for coupling S and S' to S''

S =

S' =

S'' =

5. Generate list of first n irreps of SU(N)

N =

n =

6. Generate list of all states M of irrep S

S =

7. Find index P(S) and dimension dim(S) of irrep S

S =

8. Find which irrep S is indexed by P

N =

P(S) =

9. Find index Q(M) of state M in irrep S

10. Find which state M is indexed by Q in irrep S

S =

Q(M) =


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