<< C:\drorbn\AcademicPensieve\Projects\Mathematica\LinAlg.m

rrt1 = Total[(Signature[#]*(P1@#))& /@ Permutations[{1,2,3}]];
rrt = Expand[rrt1*(rrt1 /. P1 -> P2)] /. P1[p1_]P2[p2_] :> (
P@@(p1~Join~(p2+3)) - P@@((p1+3)~Join~p2)
)

lam4[l_List] := Total[
(P[1,2,3,4,5,6] /. Thread[l -> #]& /@ Permutations[l]) /. 
p_P :> Signature[p]*p
];
lam4[i_,j_] := lam4[Complement[Range[6], {i,j}]];

lam4[3,5]

AllPs = (P@@#)& /@ Permutations[{1,2,3,4,5,6}];

LC2SA[AllPs, {lam4[3,5]}]