proposition: Lemma cfdot_prTIirr_red i j k : '[mu2_ i j, mu_ k] = (j == k)%:R.
proof: Proof. rewrite cfdot_sumr (bigD1 i) // cfdot_prTIirr eqxx /=. rewrite big1 ?addr0 // => i1 neq_i1i. by rewrite cfdot_prTIirr eq_sym (negPf neq_i1i). Qed.
imports: mathcomp.ssreflect.ssreflect mathcomp(ssrbool ssrfun eqtype ssrnat seq path div choice fintype) mathcomp(tuple finfun bigop order prime ssralg poly finset fingroup) mathcomp(morphism perm automorphism quotient action gfunctor gproduct) mathcomp(center commutator zmodp cyclic pgroup nilpotent hall frobenius) mathcomp(matrix mxalgebra mxrepresentation vector ssrnum algC classfun) mathcomp(character inertia vcharacter) odd_order(PFsection1 PFsection2 PFsection3)