diff --git a/Hamiltonian.jl b/Hamiltonian.jl
index 324346c..83d232c 100644
--- a/Hamiltonian.jl
+++ b/Hamiltonian.jl
@@ -9,6 +9,9 @@ struct Hamiltonian{T}
     K_partial::Matrix{Complex{T}}
     K_diag::Union{CuTensor{Complex{T}},Nothing}
     K_mixed::Union{CuTensor{Complex{T}},Nothing}
+    K_partial_1x::Union{Matrix{Complex{T}},Nothing}
+    K_partial_1y::Union{Matrix{Complex{T}},Nothing}
+    K_partial_1z::Union{Matrix{Complex{T}},Nothing}
     Vs::Union{Array{Complex{T}},CuArray{Complex{T}}}
     hermitian::Bool
     mode::Hamiltonian_backend
@@ -16,25 +19,27 @@ struct Hamiltonian{T}
     function Hamiltonian{T}(s::system{T}, V_twobody::Function, ϕ::Real, n_image::Int, mode::Hamiltonian_backend) where {T<:Float}
         @assert mode != gpu_cutensor || CUDA.functional() && CUDA.has_cuda() && CUDA.has_cuda_gpu() "CUDA not available"
         k = -s.N÷2:s.N÷2-1
-        Vs = calculate_Vs(s, V_twobody, convert(T, ϕ), n_image)
         hermitian = ϕ == 0.0
         K_partial = (exp(-im * convert(T, ϕ)) * im / sqrt(2 * s.μ)) .* ∂_1DOF.(Ref(s), k, k')
-        K_diag = nothing
-        K_mixed = nothing
+        K_partial_1x, K_partial_1y, K_partial_1z = sym_reduce(s, K_partial)
+        Vs = calculate_Vs(s, V_twobody, convert(T, ϕ), n_image)
         if mode == gpu_cutensor
             K_diag = CuTensor(CuArray(K_partial * K_partial), ['a', 'A'])
             K_mixed = CuTensor(CuArray(K_partial), ['a', 'A']) * CuTensor(CuArray(K_partial), ['b', 'B'])
             Vs = CuArray(Vs)
+        else
+            K_diag = nothing
+            K_mixed = nothing    
         end
-        return new{T}(s, K_partial, K_diag, K_mixed, Vs, hermitian, mode)
+        return new{T}(s, K_partial, K_diag, K_mixed, K_partial_1x, K_partial_1y, K_partial_1z, Vs, hermitian, mode)
     end
 end
 
-Base.size(H::Hamiltonian, i::Int)::Int = (i == 1 || i == 2) ? H.s.N^(H.s.d * (H.s.n - 1)) : throw(ArgumentError("Hamiltonian only has 2 dimesions"))
+Base.size(H::Hamiltonian, i::Int)::Int = (i == 1 || i == 2) ? H.s.N^(H.s.d * (H.s.n - 2)) * H.dim1 : throw(ArgumentError("Hamiltonian only has 2 dimesions"))
 Base.size(H::Hamiltonian)::Dims{2} = (size(H, 1), size(H, 2))
 
 "Dimensions of a vector to which 'H' can be applied"
-vectorDims(H::Hamiltonian)::Dims = tuple(fill(H.s.N, H.s.d * (H.s.n - 1))...)
+vectorDims(H::Hamiltonian)::Dims = tuple(H.dim1, fill(H.s.N, H.s.d * (H.s.n - 2))...)
 
 "Apply 'H' on 'v' and store the result in 'out' using the 'cpu_tensor' backend"
 function LinearAlgebra.mul!(out::Array{Complex{T}}, H::Hamiltonian{T}, v::Array{Complex{T}})::Array{Complex{T}} where {T<:Float}
@@ -47,18 +52,23 @@ function LinearAlgebra.mul!(out::Array{Complex{T}}, H::Hamiltonian{T}, v::Array{
     for dim = 1:H.s.d
         for coord1 = 1:coords
             for coord2 = 1:coord1
-                i1 = which_index(H.s, dim, coord1)
-                i2 = which_index(H.s, dim, coord2)
-                nconList_1 = [-i1, 1]
-                nconList_2 = [-i2, 2]
-                nconList_v = copy(nconList_v_template)
-                if i1 == i2
-                    nconList_2[1] = 1
+                    
+                if coord1 == 1 && coord2 == 1
+                
                 else
-                    nconList_v[i1] = 1
+                    i1 = which_index(H.s, dim, coord1)
+                    i2 = which_index(H.s, dim, coord2)
+                    nconList_1 = [-i1, 1]
+                    nconList_2 = [-i2, 2]
+                    nconList_v = copy(nconList_v_template)
+                    if i1 == i2
+                        nconList_2[1] = 1
+                    else
+                        nconList_v[i1] = 1
+                    end
+                    nconList_v[i2] = 2
+                    v_new = @ncon((H.K_partial, H.K_partial, v), (nconList_1, nconList_2, nconList_v))
                 end
-                nconList_v[i2] = 2
-                v_new = @ncon((H.K_partial, H.K_partial, v), (nconList_1, nconList_2, nconList_v))
                 out = axpy!(1, v_new, out)
             end
         end
diff --git a/common.jl b/common.jl
index aae050d..d55f901 100644
--- a/common.jl
+++ b/common.jl
@@ -1,4 +1,7 @@
+include("irrep.jl")
+
 Float = Union{Float32,Float64}
+@enum rep all A1
 
 "A few-body system defined by its physical parameters"
 struct system{T}
@@ -8,7 +11,22 @@ struct system{T}
     L::T
     μ::T
 
-    system{T}(d::Int, n::Int, N::Int, L::Real, μ::Real=0.5) where {T<:Float} = new{T}(d, n, N, convert(T, L), convert(T, μ))
+    sym::rep
+    unique_i::Array{Int}
+    unique_point::Array{Int}
+    multiplicity::Array{Int}
+
+    function system{T}(d::Int, n::Int, N::Int, L::Real, μ::Real=0.5, sym::rep=all) where {T<:Float}
+        @assert d == 3 "Only supports 3D"
+        if sym == all
+            unique_i, unique_point, multiplicity = calculate_all_data(N)
+        elseif sym == A1
+            unique_i, unique_point, multiplicity = calculate_A1_data(N)
+        else
+            throw(ArgumentError("Symmetry not yet implemented"))
+        end
+        return new{T}(d, n, N, convert(T, L), convert(T, μ), sym, unique_i, unique_point, multiplicity)
+    end
 end
 
 norm_square(x::Array{Int})::Int = sum(x .* x)
@@ -23,18 +41,27 @@ function ∂_1DOF(s::system{T}, k::Int, l::Int)::Complex{T} where {T<:Float}
 end
 
 "Which index (dimension of the multidimensional array) corresponds to spatial dimension 'dim' and particle 'p'?"
-which_index(s::system, dim::Int, p::Int)::Int = (dim - 1) * (s.n - 1) + p
+which_index(s::system, dim::Int, p::Int)::Int = (dim - 1) * (s.n - 2) + p + 1
+
+"Δk (distance in terms of lattice paramter) between two particles along the given dimension"
+function get_k(s::system, i::CartesianIndex, dim::Int, p::Int)::Int
+    if p == 1
+        s.unique_point[i[1], dim]
+    else
+        return i[which_index(s, dim, p)] - s.N ÷ 2 - 1
+    end
+end
 
 "Δk (distance in terms of lattice paramter) between two particles along the given dimension"
 function get_Δk(s::system, i::CartesianIndex, dim::Int, p1::Int, p2::Int)::Int
     if p1 == p2
         return 0
     elseif p1 == s.n
-        return -(i[which_index(s, dim, p2)] - s.N ÷ 2 - 1)
+        return -get_k(s, i, dim, p2)
     elseif p2 == s.n
-        return i[which_index(s, dim, p1)] - s.N ÷ 2 - 1
+        return get_k(s, i, dim, p1)
     else
-        return i[which_index(s, dim, p1)] - i[which_index(s, dim, p2)]
+        return get_k(s, i, dim, p1) - get_k(s, i, dim, p2)
     end
 end
 
@@ -42,7 +69,7 @@ end
 function calculate_Vs(s::system{T}, V_twobody::Function, ϕ::T, n_image::Int)::Array{Complex{T}} where {T<:Float}
     coeff² = (exp(im * ϕ) * s.L / s.N)^2
     images = collect.(Iterators.product(fill(-n_image:n_image, s.d)...)) # TODO: Learn how to use tuples instead of vectors
-    Vs = zeros(Complex{T}, fill(s.N, s.d * (s.n - 1))...)
+    Vs = zeros(Complex{T}, length(s.unique_i), fill(s.N, s.d * (s.n - 2))...)
     Threads.@threads for i in CartesianIndices(Vs)
         for p1 in 1:s.n
             for p2 in (p1 + 1):s.n
diff --git a/irrep.jl b/irrep.jl
index 249d19f..d1a4935 100644
--- a/irrep.jl
+++ b/irrep.jl
@@ -1,9 +1,18 @@
-using DelimitedFiles
-rotations = readdlm("rotations.mat", ',', Int, '\n')
-rotations = reshape(rotations, (24, 3, 3))
+using DelimitedFiles, LinearAlgebra, StatsBase
 
-function get_A1_labels(N::Int)
-    rotations = readdlm("rotations.csv", ',', Int, '\n')
+function calculate_all_data(N::Int)
+    ks = -N÷2:N÷2-1
+    lattice = hcat((collect.(Iterators.product(ks, ks, ks)))...)
+
+    unique_i = collect(1:N^3)
+    multiplicity = fill(1, length(unique_i))
+    unique_point = transpose(lattice)
+
+    return unique_i, unique_point, multiplicity
+end
+
+function calculate_A1_data(N::Int)
+    rotations = readdlm("rotations.mat", ',', Int, '\n')
     rotations = reshape(rotations, (24, 3, 3))
     
     ks = -N÷2:N÷2-1
@@ -25,9 +34,42 @@ function get_A1_labels(N::Int)
         end
     end
 
-    return labels
+    unique_i = unique(labels)
+    multiplicity = countmap(labels)
+    unique_point = transpose(lattice[unique_i, :])
+
+    return unique_i, unique_point, multiplicity
 end
 
-function sym_reduce(N::Int, K_full)
-    
+function sym_reduce(s, K_partial)
+    I = one(K_partial)
+    K_partial_x = kron(kron(K_partial, I), I)
+    K_partial_y = kron(kron(I, K_partial), I)
+    K_partial_z = kron(kron(I, I), K_partial)
+
+#    for s in 1:N^3
+#        if labels[s] != s
+#            for mat in (K_partial_x, K_partial_y, K_partial_z)
+#                mat[labels[s], :] += mat[s, :]
+#                mat[s, :] = 0
+#                mat[:, labels[s]] += mat[:, s]
+#                mat[:, s] = 0
+#            end
+#        end
+#    end
+
+    for i in s.unique_i
+        K_partial_x[i, :] *= s.multiplicity[i]
+        K_partial_x[:, i] *= s.multiplicity[i]
+        K_partial_y[i, :] *= s.multiplicity[i]
+        K_partial_y[:, i] *= s.multiplicity[i]
+        K_partial_z[i, :] *= s.multiplicity[i]
+        K_partial_z[:, i] *= s.multiplicity[i]
+    end
+
+    K_partial_x = K_partial_x[s.unique_i, s.unique_i]
+    K_partial_y = K_partial_y[s.unique_i, s.unique_i]
+    K_partial_z = K_partial_z[s.unique_i, s.unique_i]
+
+    return K_partial_x, K_partial_y, K_partial_z
 end
\ No newline at end of file
diff --git a/testing-irrep.ipynb b/testing-irrep.ipynb
new file mode 100644
index 0000000..5fcb587
--- /dev/null
+++ b/testing-irrep.ipynb
@@ -0,0 +1,49 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "include(\"Hamiltonian.jl\")\n",
+    "\n",
+    "println(\"Running with \",Threads.nthreads(),\" thread(s)\")\n",
+    "\n",
+    "T=Float32\n",
+    "\n",
+    "function V_test(r2)\n",
+    "    return -4*exp(-r2/4)\n",
+    "end\n",
+    "\n",
+    "n = 2\n",
+    "N = 16\n",
+    "println(\"\\n$n-body system with N=$N\")\n",
+    "\n",
+    "for L::T in 5.0:9.0\n",
+    "    print(\"L=$L\")\n",
+    "    s=system{T}(3,n,N,L,0.5,all)\n",
+    "    @time H=Hamiltonian{T}(s,V_test,0,0,cpu_tensor)\n",
+    "    #evals,_,_ = eig(H,5)\n",
+    "    #println(real.(evals))\n",
+    "end"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Julia 1.9.0",
+   "language": "julia",
+   "name": "julia-1.9"
+  },
+  "language_info": {
+   "file_extension": ".jl",
+   "mimetype": "application/julia",
+   "name": "julia",
+   "version": "1.9.0"
+  },
+  "orig_nbformat": 4
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}