A Gelfand model for a finite group G is a complex representation of G, which is isomorphic to the direct sum of all irreducible representations of G. When G is isomorphic to a subgroup of GL n C , where C is the field of complex numbers, it has been proved that each G-module over C is isomorphic to a G-submodule in the polynomial ring C x 1 , . . . , x n , and taking the space of zeros of certain G-invariant operators in the Weyl algebra, a finite-dimensional G-space N G in C x 1 , . . . , x n can be obtained, which contains all the simple G-modules over C. This type of representation has been named polynomial model. It has been proved that when G is a Coxeter group, the polynomial model is a Gelfand model for G if, and only if, G has not an irreducible factor of type D 2n , E 7 , or E 8 . This paper presents a model of Gelfand for a Weyl group of type D 2n whose construction is based on the same principles as the polynomial model.

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