From e78da236bdb052f760c2bc04a93327b87a8daf6b Mon Sep 17 00:00:00 2001
From: Sheehan Olver <solver@mac.com>
Date: Fri, 17 Nov 2023 08:57:58 +0000
Subject: [PATCH] Fix identity rep (#4)

* Fix identity representation

* Update NumericalRepresentationTheory.jl

* Update Project.toml
---
 Project.toml                         |  2 +-
 src/NumericalRepresentationTheory.jl | 10 ++++++++--
 test/runtests.jl                     | 18 ++++++++++++------
 3 files changed, 21 insertions(+), 9 deletions(-)

diff --git a/Project.toml b/Project.toml
index ce46da8..4db3d8a 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "NumericalRepresentationTheory"
 uuid = "6b7c1d51-ecee-4149-97a8-50646b514dce"
 authors = ["Sheehan Olver <solver@mac.com>"]
-version = "0.1.0"
+version = "0.1.1"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
diff --git a/src/NumericalRepresentationTheory.jl b/src/NumericalRepresentationTheory.jl
index 448f36c..cc42343 100644
--- a/src/NumericalRepresentationTheory.jl
+++ b/src/NumericalRepresentationTheory.jl
@@ -287,8 +287,14 @@ diagm(A::Vector{<:Representation}) = Representation(blockdiag.(generators.(A)...
 ⊕(A::Representation...) = Representation(blockdiag.(generators.(A)...))
 
 
-(R::Representation)(P::AbstractPermutation) =
-    *(map(i -> R.generators[i], CoxeterDecomposition(P).terms)...)
+function (R::Representation)(P::AbstractPermutation)
+    if isempty(CoxeterDecomposition(P).terms)
+        # Identity
+        one(first(R.generators))
+    else
+        *(map(i -> R.generators[i], CoxeterDecomposition(P).terms)...)
+    end
+end
 
 # determine multiplicities of eigs on diagonal, assuming sorted
 function eigmults(λ::Vector{Int})
diff --git a/test/runtests.jl b/test/runtests.jl
index 9924429..28e28b2 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,4 +1,4 @@
-using NumericalRepresentationTheory, LinearAlgebra, Test
+using NumericalRepresentationTheory, Permutations, LinearAlgebra, Test
 import NumericalRepresentationTheory: gelfandbasis
 
 @testset "Representations" begin
@@ -36,12 +36,18 @@ import NumericalRepresentationTheory: gelfandbasis
         @test multiplicities(ρ̃) == multiplicities(ρ)
         @test abs.(blockdiagonalize(ρ̃)[2]) ≈ abs.(Matrix(Q))
     end
+
+    @testset "Rico Bug" begin
+        ρ = Representation(2,1)
+        g = Permutation([1,2,3])
+        @test ρ(g) == I(2)
+    end
 end
 
 
-basis = gelfandbasis(Representation(Partition([3,2,1])).generators)
-Λ = Matrix{Int}(undef, size(basis[1],1), length(basis))
-for k in axes(Λ,1), j in axes(Λ,2)
-    Λ[k,j] = round(Int,basis[j][k,k])
-end
+# basis = gelfandbasis(Representation(Partition([3,2,1])).generators)
+# Λ = Matrix{Int}(undef, size(basis[1],1), length(basis))
+# for k in axes(Λ,1), j in axes(Λ,2)
+#     Λ[k,j] = round(Int,basis[j][k,k])
+# end