proposition: Lemma omegasfK : involutive omegasf.
proof: Proof. move=> p; rewrite -(sympolyfK p). rewrite (mpolyE (sympolyf p)); move: (sympolyf p) => q. rewrite [sympolyf_eval _]raddf_sum !raddf_sum /=; apply eq_bigr => mon _. rewrite !linearZ /=; congr (_ *: _). rewrite mpolyXE_id !rmorph_prod /=; apply eq_bigr => i _. rewrite !rmorphXn /=; congr ( _ ^+ _). by rewrite sympolyf_evalX omegasf_syme // omegasf_symh. Qed.
imports: HB(structures) mathcomp(all_ssreflect) mathcomp(ssralg ssrint fingroup perm) mathcomp(ssrcomplements freeg mpoly) sorted tools ordtype permuted partition skewpart composition Yamanouchi std tableau stdtab skewtab permcent antisym Schur_mpoly therule Schur_altdef unitriginv