proposition: Lemma syms_syme_partdom mu : 's[mu^~] = 'e[mu] + \sum_(la | (mu < la :> 'PDom_d)%O) 'K^-1(la, mu) *: 'e[la] :> SF.
proof: Proof. rewrite -(map_syms intr) syms_syme_partdom_int. rewrite rmorphD rmorph_sum /= map_syme_prod; congr (_ + _); apply eq_bigr => i _. by rewrite linearZ_LR /= map_syme_prod. 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