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arXiv · 0711.4494

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

Loïc Foissy
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Abstract

Let G be a Coxeter group of type A_n, B_n, D_n or I_2(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)^{\otimes k}. We show that the algebra of invariants (S(V)^{\otimes k})^G is a free (S(V)^G)^{\otimes k}-module of rank |G|^{k-1}, and that S(V)^{\otimes k} is not a free (S(V)^{\otimes k})^G-module.

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Loïc Foissy. 2007-11-28. L'algèbre des invariants d'un groupe de Coxeter agissant sur un mutiple de sa représentation standard. https://arxiv.org/abs/0711.4494

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