L'algèbre des invariants d'un groupe de Coxeter agissant sur un mutiple de sa représentation standard

الأصل · EN

Let G be a Coxeter group of type Aₙ, Bₙ, Dₙ or I₂(N), or a complex reflection group of type G(de,e,n). Let V be its standard representation and let k be an integer greater than 2. Then G acts on S(V)⊗ ᵏ. We show that the algebra of invariants (S(V)⊗ ᵏ)ᵍ is a free (S(V)ᵍ)⊗ ᵏ-module of rank |G|ᵏ⁻¹, and that S(V)⊗ ᵏ is not a free (S(V)⊗ ᵏ)ᵍ-module.