# Load the SF package
with(SF);

# computes s_\la s_\mu but with the restriction that no partition in
# the result has length longer than length(\la)
restrmult:=proc(la,mu) local sEX, sids, v;
 sEX:=tos(s[op(la)]*s[op(mu)]);
 sids:=select(x->evalb(nops(x)>nops(la)),
 select(x->evalb(op(0,x)=`s`),indets(sEX,`indexed`)));
 subs({seq(v=0,v=sids)},sEX);
end:

# The creation operator \widetilde{ B_\mu } which builds the
# generalized Hall-Littlewood symmetric functions.
# remark: theta(theta(s_\la,q,0),-1) = s_\la[(q-1)X]
Bmutilde:=proc(mu,EX) local n, ga;
tos(s[op(mu)]*EX+add(add(restrmult(mu,ga)*skew(
theta(theta(s[op(ga)],q,0),-1),EX), ga=Par(n,nops(mu))),
n=1..stdeg(EX)));
end:

# The generalized Hall-Littlewood functions $H_{(\mu^{(1)},..,\mu^{(k)})}[X;q]$
H:=proc(partlst) local out,i;
out:=s[op(partlst[-1])];
for i from 2 to nops(partlst) do
  out:=Bmutilde(partlst[-i],out);
od;
out;
end:

# Example
Bmutilde([2,1],s[1]);
H([[3,2],[2,1],[1]]);