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tensor_from_table

Function tensor_from_table 

Source
pub fn tensor_from_table(t: &CharacterTable) -> Option<Vec<Vec<Vec<u128>>>>
Expand description

The tensor (Clebsch–Gordan) decomposition of the irreducibles: N[i][j][k] = ⟨χ_i·χ_j, χ_k⟩, the multiplicity of χ_k in the tensor product χ_i ⊗ χ_j. These are the fusion coefficients — the structure constants of the representation ring R(G) (the multiplication dual to the character table’s addition). Computed from a character table: N[i][j][k] = (1/|G|) Σ_r |C_r|·χ_i(C_r)·χ_j(C_r)·χ_k(C_{r̄}) over the table’s GF(p); each is a small non-negative integer ≤ d_i·d_j ≤ |G| < p, so it decodes uniquely. FAIL-CLOSED: returns None unless every fusion product has the right dimension (Σ_k N[i][j][k]·d_k = d_i·d_j), the trivial character is a unit (χ_triv ⊗ χ_j = χ_j), and the coefficients are symmetric (N[i][j][k] = N[j][i][k]). Indices align with character_table’s rows.