kalmar/PropertyT.jl
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account for changes in order of characters

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kalmar 2017-07-17 12:27:28 +02:00
parent 4e48917a38
commit 6ecd63197b
1 changed files with 22 additions and 20 deletions
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40
src/Projections.jl
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@ -29,26 +29,27 @@ end
function rankOne_projections(G::PermutationGroup, T::Type=Rational{Int}) function rankOne_projections(G::PermutationGroup, T::Type=Rational{Int})
RG = GroupRing(G) RG = GroupRing(G)
projections = [central_projection(RG, χ, T) for χ in chars(G)] cprojs = [central_projection(RG, χ, T) for χ in (character(λ) for λ in IntPartitions(G.n))]
if G.n == 1 || G.n == 2 if G.n == 1 || G.n == 2
return projections return cprojs
elseif G.n == 3 elseif G.n == 3
p = 1//2*(one(RG, T) - RG(G([2,1,3]), T))
rankone_projs = [ rankone_projs = [
projections[1], cprojs[1], # alternating
projections[2], p*cprojs[2], # regular
1//2*(one(RG, T) - RG(G([2,1,3]), T))*projections[3] cprojs[3] # trivial
] ]
return rankone_projs
elseif G.n == 4 elseif G.n == 4
p⁺ = 1//2*(one(RG, T) + RG(G([2,1,3,4]), T))
p⁻ = 1//2*(one(RG, T) - RG(G([2,1,3,4]), T))
rankone_projs = [ rankone_projs = [
projections[1], cprojs[1], # alternating
projections[2], p⁺*cprojs[2], # alt_regular
1//2*(one(RG, T) - RG(G([2,1,3,4]), T))*projections[3], p⁻*cprojs[3], # regular
1//2*(one(RG, T) - RG(G([2,1,3,4]), T))*projections[4], p⁻*cprojs[4], # via projection to S₃
1//2*(one(RG, T) + RG(G([2,1,3,4]), T))*projections[5] cprojs[5] # trivial
] ]
return rankone_projs
elseif G.n == 5 elseif G.n == 5
p⁺ = 1//2*(one(RG, T) + RG(G([2,1,3,4,5]), T)) p⁺ = 1//2*(one(RG, T) + RG(G([2,1,3,4,5]), T))
p⁻ = 1//2*(one(RG, T) - RG(G([2,1,3,4,5]), T)) p⁻ = 1//2*(one(RG, T) - RG(G([2,1,3,4,5]), T))
@ -57,17 +58,18 @@ function rankOne_projections(G::PermutationGroup, T::Type=Rational{Int})
q⁻ = 1//2*(one(RG, T) - RG(G([1,2,4,3,5]), T)) q⁻ = 1//2*(one(RG, T) - RG(G([1,2,4,3,5]), T))
rankone_projs = [ rankone_projs = [
projections[1], cprojs[1], # alternating
projections[2], p⁺*cprojs[2], # alt_regular
p⁻*projections[3], p⁺*q⁺*cprojs[3], # ψ
p⁺*projections[4], p⁻*q⁻*cprojs[4], # alt_ϱ
p⁺*q⁺*projections[5], p⁻*cprojs[5], # regular
p⁻*q⁻*projections[6], p⁺*q⁺*cprojs[6], # ϱ
p⁺*q⁺*projections[7] cprojs[7] # trivial
] ]
else else
throw("Rank-one projections for $G unknown!") throw("Rank-one projections for $G unknown!")
end end
return rankone_projs
end end
function rankOne_projections(BN::WreathProduct, T::Type=Rational{Int}) function rankOne_projections(BN::WreathProduct, T::Type=Rational{Int})