Adapt return type; add more methods

oscar-system · Nov 26, 2024 · 3e3b610 · 3e3b610
1 parent 9943757
commit 3e3b610
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Showing 4 changed files with 486 additions and 220 deletions.
diff --git a/experimental/LieAlgebras/src/LieAlgebraModule.jl b/experimental/LieAlgebras/src/LieAlgebraModule.jl
@@ -1553,6 +1553,56 @@ function character(L::LieAlgebra, hw::WeightLatticeElem)
   return character(R, hw)
 end
 
+function demazure_character(L::LieAlgebra, w::WeightLatticeElem, x::WeylGroupElem)
+  return demazure_character(root_system(L), w, x)
+end
+
+function demazure_character(
+  T::DataType, L::LieAlgebra, w::WeightLatticeElem, x::WeylGroupElem
+)
+  return demazure_character(T, root_system(L), w, x)
+end
+
+function demazure_character(
+  L::LieAlgebra, w::WeightLatticeElem, reduced_expression::Vector{<:IntegerUnion}
+)
+  return demazure_character(root_system(L), w, reduced_expression)
+end
+
+function demazure_character(
+  T::DataType,
+  L::LieAlgebra,
+  w::WeightLatticeElem,
+  reduced_expression::Vector{<:IntegerUnion},
+)
+  return demazure_character(T, root_system(L), w, reduced_expression)
+end
+
+function demazure_character(L::LieAlgebra, w::Vector{<:IntegerUnion}, x::WeylGroupElem)
+  return demazure_character(root_system(L), w, x)
+end
+
+function demazure_character(
+  T::DataType, L::LieAlgebra, w::Vector{<:IntegerUnion}, x::WeylGroupElem
+)
+  return demazure_character(T, root_system(L), w, x)
+end
+
+function demazure_character(
+  L::LieAlgebra, w::Vector{<:IntegerUnion}, reduced_expression::Vector{<:IntegerUnion}
+)
+  return demazure_character(root_system(L), w, reduced_expression)
+end
+
+function demazure_character(
+  T::DataType,
+  L::LieAlgebra,
+  w::Vector{<:IntegerUnion},
+  reduced_expression::Vector{<:IntegerUnion},
+)
+  return demazure_character(T, root_system(L), w, reduced_expression)
+end
+
 @doc raw"""
     tensor_product_decomposition(L::LieAlgebra, hw1::Vector{<:IntegerUnion}, hw2::Vector{<:IntegerUnion}) -> MSet{Vector{Int}}
     tensor_product_decomposition(L::LieAlgebra, hw1::WeightLatticeElem, hw2::WeightLatticeElem) -> MSet{Vector{Int}}

diff --git a/experimental/LieAlgebras/src/RootSystem.jl b/experimental/LieAlgebras/src/RootSystem.jl
@@ -2178,17 +2178,62 @@ function demazure_operator(r::RootSpaceElem, groupringelem::Dict{WeightLatticeEl
   return dict
 end
 
-function demazure_character(w::WeightLatticeElem, x::WeylGroupElem)
-  reduced_expression = word(x)
-  character = Dict{WeightLatticeElem,Int}(w => 1)
+function demazure_character(R::RootSystem, w::WeightLatticeElem, x::WeylGroupElem)
+  @req root_system(parent(x)) === R "parent root system mismatch"
+  return demazure_character(R, w, word(x))
+end
+
+function demazure_character(
+  T::DataType, R::RootSystem, w::WeightLatticeElem, x::WeylGroupElem
+)
+  @req root_system(parent(x)) === R "parent root system mismatch"
+  return demazure_character(T, R, w, word(x))
+end
+
+function demazure_character(
+  R::RootSystem, w::WeightLatticeElem, reduced_expression::Vector{<:IntegerUnion}
+)
+  return demazure_character(Int, R, w, reduced_expression)
+end
+
+function demazure_character(
+  T::DataType,
+  R::RootSystem,
+  w::WeightLatticeElem,
+  reduced_expression::Vector{<:IntegerUnion},
+)
+  @req root_system(w) === R "parent root system mismatch"
+  @req is_dominant(w) "not a dominant weight"
+  char = Dict{WeightLatticeElem,T}(w => T(1))
   for i in Iterators.reverse(reduced_expression)
-    character = demazure_operator(simple_root(root_system(w), Int(i)), character)
+    char = demazure_operator(simple_root(root_system(w), Int(i)), char)
   end
-  return Dict(Int.(_vec(coefficients(w_))) => m for (w_, m) in character)
+  return char
 end
 
-function demazure_character(R::RootSystem, hw::Vector{<:IntegerUnion}, x::WeylGroupElem)
-  return demazure_character(WeightLatticeElem(R, hw), x)
+function demazure_character(R::RootSystem, w::Vector{<:IntegerUnion}, x::WeylGroupElem)
+  return demazure_character(R, WeightLatticeElem(R, w), x)
+end
+
+function demazure_character(
+  T::DataType, R::RootSystem, w::Vector{<:IntegerUnion}, x::WeylGroupElem
+)
+  return demazure_character(T, R, WeightLatticeElem(R, w), x)
+end
+
+function demazure_character(
+  R::RootSystem, w::Vector{<:IntegerUnion}, reduced_expression::Vector{<:IntegerUnion}
+)
+  return demazure_character(R, WeightLatticeElem(R, w), reduced_expression)
+end
+
+function demazure_character(
+  T::DataType,
+  R::RootSystem,
+  w::Vector{<:IntegerUnion},
+  reduced_expression::Vector{<:IntegerUnion},
+)
+  return demazure_character(T, R, WeightLatticeElem(R, w), reduced_expression)
 end
 
 ###############################################################################

diff --git a/experimental/LieAlgebras/src/exports.jl b/experimental/LieAlgebras/src/exports.jl
@@ -39,6 +39,7 @@ export conjugate_dominant_weight_with_right_elem
 export coroot
 export coroots
 export coxeter_matrix
+export demazure_character
 export demazure_operator
 export derived_algebra
 export dim_of_simple_module