Dihedral group representations (#24)

* Reorganize irreps into separate files

* Add `D{N}`

* Add `DNIrrep`

* Add property accessors

* Add Sector iterator

* Add Sector product iterator

* Add Nsymbol and dim

* Add one

* Reorganization

* Add topological data

* Add tests

* Add `D3Irrep` and `D4Irrep`

* small fixes

* Add orthogonality tests

* Change group type aliases

* clearer error message

* Explicit 3-argument indexing

* Move sqrt(2)/2

* Change `iseven(N)` checks

* Remove unparseable show method

Author: lkdvos

src/TensorKitSectors.jl

@@ -17,7 +17,10 @@ export rightone, leftone
 
 export triangle_equation, pentagon_equation, hexagon_equation
 
-export Trivial, Z2Irrep, Z3Irrep, Z4Irrep, ZNIrrep, U1Irrep, SU2Irrep, CU1Irrep
+export Trivial
+export Z2Irrep, Z3Irrep, Z4Irrep, ZNIrrep, U1Irrep
+export D3Irrep, D4Irrep, DNIrrep, CU1Irrep
+export SU2Irrep
 export ZNElement, Z2Element, Z3Element, Z4Element
 export ProductSector, TimeReversed
 export FermionParity, FermionNumber, FermionSpin
@@ -27,7 +30,7 @@ export IsingBimodule
 # unicode exports
 # ---------------
 export ⊠, ⊗, ×
-export ℤ, ℤ₂, ℤ₃, ℤ₄, U₁, SU, SU₂, CU₁
+export Cyclic, ℤ, ℤ₂, ℤ₃, ℤ₄, U₁, SU, SU₂, Dihedral, D₃, D₄, CU₁
 export fℤ₂, fU₁, fSU₂
 
 # imports
@@ -48,7 +51,7 @@ include("auxiliary.jl")
 include("sectors.jl")
 include("trivial.jl")
 include("groups.jl")
-include("irreps.jl")    # irreps of symmetry groups, with bosonic braiding
+include("irreps/irreps.jl")    # irreps of symmetry groups, with bosonic braiding
 include("groupelements.jl") # group elements with cocycles, no braiding
 include("product.jl")   # direct product of different sectors
 include("fermions.jl")  # irreps with defined fermionparity and fermionic braiding

src/groups.jl

@@ -3,19 +3,25 @@
 abstract type Group end
 abstract type AbelianGroup <: Group end
 
-abstract type ℤ{N} <: AbelianGroup end
+abstract type Cyclic{N} <: AbelianGroup end
 abstract type U₁ <: AbelianGroup end
 abstract type SU{N} <: Group end
 abstract type CU₁ <: Group end
+abstract type Dihedral{N} <: Group end
 
+const ℤ{N} = Cyclic{N}
 const ℤ₂ = ℤ{2}
 const ℤ₃ = ℤ{3}
 const ℤ₄ = ℤ{4}
+const D₃ = Dihedral{3}
+const D₄ = Dihedral{4}
 const SU₂ = SU{2}
 
 type_repr(::Type{ℤ₂}) = "ℤ₂"
 type_repr(::Type{ℤ₃}) = "ℤ₃"
 type_repr(::Type{ℤ₄}) = "ℤ₄"
+type_repr(::Type{D₃}) = "D₃"
+type_repr(::Type{D₄}) = "D₄"
 type_repr(::Type{SU₂}) = "SU₂"
 type_repr(T::Type) = repr(T)