diff --git a/experimental/BasisLieHighestWeight/src/MainAlgorithm.jl b/experimental/BasisLieHighestWeight/src/MainAlgorithm.jl
index e35f7aab42b5..90b4b8f38153 100644
--- a/experimental/BasisLieHighestWeight/src/MainAlgorithm.jl
+++ b/experimental/BasisLieHighestWeight/src/MainAlgorithm.jl
@@ -379,18 +379,18 @@ function operators_by_simple_roots(
   return operators_by_index(L, chevalley_basis, root_inds)
 end
 
-function operators_lustzig(
+function operators_lusztig(
   L::LieAlgebraStructure,
   chevalley_basis::NTuple{3,Vector{GAP.Obj}},
   reduced_expression::Vector{Int},
 )
-  root_inds = operators_lustzig_indices(L, reduced_expression)
+  root_inds = operators_lusztig_indices(L, reduced_expression)
   return operators_by_index(L, chevalley_basis, root_inds)
 end
 
-function operators_lustzig_indices(L::LieAlgebraStructure, word::Vector{Int})
+function operators_lusztig_indices(L::LieAlgebraStructure, word::Vector{Int})
   """
-  Computes the operators for the lustzig polytopes for a longest weyl-word 
+  Computes the operators for the lusztig polytopes for a longest weyl-word 
   reduced_expression.
 
   \beta_k := s_{i_1} … s_{i_{k-1}} (\alpha_{i_k})
diff --git a/experimental/BasisLieHighestWeight/src/UserFunctions.jl b/experimental/BasisLieHighestWeight/src/UserFunctions.jl
index 93da8d2f7a98..a4c6355624cf 100644
--- a/experimental/BasisLieHighestWeight/src/UserFunctions.jl
+++ b/experimental/BasisLieHighestWeight/src/UserFunctions.jl
@@ -165,7 +165,7 @@ end
 @doc """
 # Examples
 ```jldoctest
-julia> base = BasisLieHighestWeight.basis_lie_highest_weight_lustzig(:D, 4, [1,1,1,1], [4,3,2,4,3,2,1,2,4,3,2,1])
+julia> base = BasisLieHighestWeight.basis_lie_highest_weight_lusztig(:D, 4, [1,1,1,1], [4,3,2,4,3,2,1,2,4,3,2,1])
 Monomial basis of a highest weight module
   of highest weight [1, 1, 1, 1]
   of dimension 4096
@@ -192,18 +192,18 @@ over lie-Algebra of type D and rank 4
     [0, 0, 1, 1]
 ```
 """
-function basis_lie_highest_weight_lustzig(
+function basis_lie_highest_weight_lusztig(
   type::Symbol, rank::Int, highest_weight::Vector{Int}, reduced_expression::Vector{Int}
 )
   """
-  Lustzig polytope
-  BasisLieHighestWeight.basis_lie_highest_weight_lustzig(:D, 4, [1,1,1,1], [4,3,2,4,3,2,1,2,4,3,2,1])
+  lusztig polytope
+  BasisLieHighestWeight.basis_lie_highest_weight_lusztig(:D, 4, [1,1,1,1], [4,3,2,4,3,2,1,2,4,3,2,1])
   """
   # operators = some sequence of the String / Littelmann-Berenstein-Zelevinsky polytope
   monomial_ordering = :wdegrevlex
   L = lie_algebra(type, rank)
   chevalley_basis = chevalley_basis_gap(L)
-  operators = operators_lustzig(L, chevalley_basis, reduced_expression)
+  operators = operators_lusztig(L, chevalley_basis, reduced_expression)
   return basis_lie_highest_weight_compute(
     L, chevalley_basis, highest_weight, operators, monomial_ordering
   )