A Gelfand model for a finite group G is a complex linear representation of G that contains each of its irreducible representations with multiplicity one. For a finite group G with a faithful representation V , one constructs a representation which we call the polynomial model for G associated to V . Araujo and others have proved that the polynomial models for certain irreducible Weyl groups associated to their canonical representations are Gelfand models. In this paper, we give an easier and

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... ve an easier and uniform treatment for the study of the polynomial model for a general finite Coxeter group associated to its canonical representation. Our final result is that such a polynomial model for a finite Coxeter group G is a Gelfand model if and only if G has no direct factor of the type W ðD 2n Þ, W ðE 7 Þ or W ðE 8 Þ. Unauthenticated Download Date | 7/28/18 12:55 PM