pub fn isotypic_from_table(
degree: usize,
gens: &[Perm],
t: &CharacterTable,
) -> Option<Vec<u128>>Expand description
The isotypic decomposition of the permutation representation: the multiplicity m_s = ⟨π, χ_s⟩ of
each irreducible χ_s in the natural action’s character π, i.e. π = Σ_s m_s χ_s. Computed from a
character table: m_s = (1/|G|) Σ_r |C_r|·π(C_r)·χ_s(C_{r̄}) over the table’s GF(p). The
representation-theoretic spectrum of the symmetry — it ties the linear theory back to the action:
m_trivial = #orbits (Burnside), Σ_s m_s² = rank (#orbitals), Σ_s m_s·d_s = degree. FAIL-CLOSED:
None if p ≤ degree (then the small non-negative m_s ≤ degree would not decode uniquely) or if any
of those three identities fails. Aligned with the table’s rows.