Forgotten vertex operators

Add a sequence of columns to f_\la[X]

> with(combinat,numbcomb):

> CF:=proc(m,k,EX);
tof(f[seq(m,i=1..k)]*EX+convert([seq(seq(
(-1)^i*numbcomb(k+mm(m,la),k)*
f[op(insrtmk(m,k,la))]*skew(hla(la),EX),
la=Par(i)),i=1..`SF/stdeg`(EX))],`+`));
end:

> insrtmk:=proc(m,k,la) local rslt,i,j;
if m>=la[1] then rslt:=[seq(m,i=1..k),op(la)];
elif la[nops(la)]>=m then
rslt:=[op(la),seq(m,i=1..k)];
else
rslt:=NULL; i:=1;
while la[i]>=m do
rslt:=rslt,la[i];i:=i+1;
od;
rslt:=[rslt,seq(m,j=1..k),seq(la[j],j=i..nops(la))];
fi;
rslt;
end:

> mm:=proc(m,la) local i;
convert([seq(eqm(la[i],m), i=1..nops(la))],`+`);
end:
eqm:=proc(n,m); if n=m then 1; else 0; fi; end:

> hla:=proc(la) local i;
product(h.(la[i]),i=1..nops(la));
end:

Add a row on f_\la[X]

> RF:=proc(k,EX) local a,b,c,i,j,la;
tof(convert([seq(seq(seq(
(-1)^j*f[seq(la[b]+k,b=1..nops(la)),seq(k,c=1..i-nops(la))]*
skew(hla(la)*(-e.k)^(i-1),EX),
la=Par(j,i)),
j=0..`SF/stdeg`(EX)-k*(i-1)),
i=1..trunc(evalf(`SF/stdeg`(EX)/k))+1)],`+`));
end:
hla:=la->product(h.(la[i]),i=1..nops(la)):
nk:=proc(k,la);
convert([seq(eqk(k,la[i]), i=1..nops(la))],`+`);
end:
eqk:=proc(n,k);
if n=k then 1; else 0; fi;
end