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big overhaul of rankOne_projections for WreathProduct Group

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kalmarek 2018-04-09 11:07:12 +02:00
parent 094abd74b8
commit 11365bf5b2
1 changed files with 33 additions and 26 deletions
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59
src/Projections.jl
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@ -146,40 +146,47 @@ function rankOne_projections(G::Generic.PermGroup, T::Type=Rational{Int})
return min_projs
end
function rankOne_projections(BN::WreathProduct, T::Type=Rational{Int})
function rankOne_projections(Bn::WreathProduct, T::Type=Rational{Int})
N = BN.P.n
N = Bn.P.n
# projections as elements of the group rings RSₙ
SNprojs_nc = [rankOne_projections(PermutationGroup(i)) for i in 1:N]
Sn_rankOnePr = [rankOne_projections(PermutationGroup(i)) for i in 1:N]
# embedding into group ring of BN
RBN = GroupRing(BN)
RFFFF_projs = [central_projection(GroupRing(BN.N), DirectProdCharacter(i),T)
for i in 1:BN.P.n]
RBn = GroupRing(Bn)
RN = GroupRing(Bn.N)
e0 = central_projection(GroupRing(BN.N), DirectProdCharacter(0), T)
Q0 = RBN(e0, g -> BN(g))
Qs = [RBN(q, g -> BN(g)) for q in RFFFF_projs]
# Bn.N = (Z/2Z)ⁿ characters corresponding to the first k coordinates:
all_projs = [Q0*RBN(p, g->BN(g)) for p in SNprojs_nc[N]]
range = collect(1:N)
for i in 1:N-1
first_emb = g->BN(Nemo.Generic.emb!(BN.P(), g, range[1:i]))
last_emb = g->BN(Nemo.Generic.emb!(BN.P(), g, range[i+1:end]))
Sk_first = [RBN(p, first_emb) for p in SNprojs_nc[i]]
Sk_last = [RBN(p, last_emb) for p in SNprojs_nc[N-i]]
append!(all_projs,
[Qs[i]*p1*p2 for (p1,p2) in Base.product(Sk_first,Sk_last)])
end
append!(all_projs, [Qs[N]*RBN(p, g->BN(g)) for p in SNprojs_nc[N]])
return all_projs
function OrbitSelector(n::Integer, k::Integer,
chi::Projections.AbstractCharacter, psi::Projections.AbstractCharacter)
return Projections.DirectProdCharacter(ntuple(i -> (i <= k ? chi : psi), n))
end
sign, id = collect(characters(Bn.N.group))
BnN_orbits = Dict(i => OrbitSelector(N, i, sign, id) for i in 0:N)
Q = Dict(i => RBn(central_projection(RN, BnN_orbits[i], T), g -> Bn(g)) for i in 0:N)
all_projs = [Q[0]*RBn(p, g->Bn(g)) for p in Sn_rankOnePr[N]]
r = collect(1:N)
for i in 1:N-1
first_emb = g->Bn(Nemo.Generic.emb!(Bn.P(), g, view(r, 1:i)))
last_emb = g->Bn(Nemo.Generic.emb!(Bn.P(), g, view(r, (i+1):N)))
Sk_first = (RBn(p, first_emb) for p in Sn_rankOnePr[i])
Sk_last = (RBn(p, last_emb) for p in Sn_rankOnePr[N-i])
append!(all_projs,
[Q[i]*p1*p2 for (p1,p2) in Base.product(Sk_first,Sk_last)])
end
append!(all_projs, [Q[N]*RBn(p, g->Bn(g)) for p in Sn_rankOnePr[N]])
return all_projs
end
##############################################################################
#
# General Groups Misc