pub fn frobenius_schur_from_table(t: &CharacterTable) -> Option<Vec<i8>>Expand description
The Frobenius–Schur indicators ν(χ_s) = (1/|G|) Σ_{g∈G} χ_s(g²) ∈ {+1, 0, −1} read off a
character table: +1 if the irreducible is real (orthogonal), 0 if complex (χ ≠ χ̄), −1
if quaternionic (symplectic). Computed exactly over the table’s GF(p):
Σ_r |C_r|·χ_s(C_{r²}), scaled by 1/|G|, decoded {0, 1, p−1} → {0, 1, −1}. FAIL-CLOSED: returns
None if any value decodes outside {−1,0,1} or the Frobenius–Schur sum rule
Σ_s ν(χ_s)·d_s = #{g : g²=1} fails. The indicators distinguish groups with identical character
tables (e.g. D₄ all +1 vs Q₈ with a −1).