braidingtensor special cases

src/fusiontrees/manipulations.jl

@@ -522,9 +522,11 @@ const TransposeKey{I<:Sector, N₁, N₂} = Tuple{<:FusionTree{I}, <:FusionTree{
 function _transpose((f1, f2, p1, p2)::TransposeKey{I,N₁,N₂}) where {I<:Sector, N₁, N₂}
     N = N₁ + N₂
     p = linearizepermutation(p1, p2, length(f1), length(f2))
+    newtrees = repartition(f1, f2, N₁)
+    length(p) == 0 && return newtrees
     i1 = findfirst(==(1), p)
     @assert i1 !== nothing
-    newtrees = repartition(f1, f2, N₁)
+    i1 == 1 && return newtrees
     Nhalf = N >> 1
     while 1 < i1 <= Nhalf
         local newtrees′
@@ -766,7 +768,38 @@ function artin_braid(f::FusionTree{I, N}, i; inv::Bool = false) where {I<:Sector
     inner = f.innerlines
     vertices = f.vertices
     u = one(I)
-    oneT = one(eltype(Rsymbol(u,u,u))) * one(eltype(Fsymbol(u,u,u,u,u,u)))
+
+    if BraidingStyle(I) isa NoBraiding
+        oneT = one(eltype(Fsymbol(u,u,u,u,u,u)))
+    else
+        oneT = one(eltype(Rsymbol(u,u,u))) * one(eltype(Fsymbol(u,u,u,u,u,u)))
+    end
+
+    if u in (uncoupled[i],uncoupled[i+1]) # the braid simplifies drastically, we are braiding a trivial sector
+        a, b = uncoupled[i], uncoupled[i+1]
+        uncoupled′ = TupleTools.setindex(uncoupled,b,i);
+        uncoupled′ = TupleTools.setindex(uncoupled′,a,i+1);
+        vertices′ = vertices;
+
+        if i > 1 #we also need to alter innerlines and vertices
+            incharges = (uncoupled[1],inner...,coupled′);
+
+            vertices′  = TupleTools.setindex(vertices′,vertices[i],i-1)
+            vertices′  = TupleTools.setindex(vertices′,vertices[i-1],i)
+
+            if a == u
+                inner = TupleTools.setindex(inner,incharges[i+1],i-1);
+            else
+                inner = TupleTools.setindex(inner,incharges[i-1],i-1);
+            end
+        end
+
+        f′ = FusionTree{I}(uncoupled′, coupled′, isdual′, inner, vertices′)
+        return fusiontreedict(I)(f′ => oneT)
+    end
+
+    BraidingStyle(I) isa NoBraiding && throw(SectorMismatch("cannot braid sector "*type_repr(I)))
+
     if i == 1
         a, b = uncoupled[1], uncoupled[2]
         c = N > 2 ? inner[1] : coupled′