change conj to dual for sectors

Author: borisdevos

src/fusiontrees/fusiontrees.jl

@@ -152,8 +152,8 @@ end
 function Base.convert(A::Type{<:AbstractArray}, f::FusionTree{I,1}) where {I}
     c = f.coupled
     if f.isdual[1]
-        sqrtdc = sqrtdim(c) # TODO: change conj to dual
-        Zcbartranspose = sqrtdc * convert(A, fusiontensor(conj(c), c, unit(c)))[:, :, 1, 1]
+        sqrtdc = sqrtdim(c)
+        Zcbartranspose = sqrtdc * convert(A, fusiontensor(dual(c), c, unit(c)))[:, :, 1, 1]
         X = conj!(Zcbartranspose) # we want Zcbar^†
     else
         X = convert(A, fusiontensor(c, unit(c), c))[:, 1, :, 1, 1]

src/fusiontrees/manipulations.jl

@@ -898,7 +898,7 @@ function artin_braid(f::FusionTree{I,N}, i; inv::Bool=false) where {I<:Sector,N}
         return fusiontreedict(I)(f′ => coeff)
     elseif FusionStyle(I) isa SimpleFusion
         local newtrees
-        for c′ in intersect(a ⊗ d, e ⊗ conj(b))
+        for c′ in intersect(a ⊗ d, e ⊗ dual(b))
             coeff = oftype(oneT,
                            if inv
                                conj(Rsymbol(d, c, e) * Fsymbol(d, a, b, e, c′, c)) *
@@ -919,7 +919,7 @@ function artin_braid(f::FusionTree{I,N}, i; inv::Bool=false) where {I<:Sector,N}
         return newtrees
     else # GenericFusion
         local newtrees
-        for c′ in intersect(a ⊗ d, e ⊗ conj(b))
+        for c′ in intersect(a ⊗ d, e ⊗ dual(b))
             Rmat1 = inv ? Rsymbol(d, c, e)' : Rsymbol(c, d, e)
             Rmat2 = inv ? Rsymbol(d, a, c′)' : Rsymbol(a, d, c′)
             Fmat = Fsymbol(d, a, b, e, c′, c)