Abstract
A Gel'fand model for a finite group G is a complex representation of G which is isomorphic to the direct sum of all the irreducible representation of G (see [8]). Gel'fand models for the linear group over a finite field can be found in [6]. In this work we describe a Gel'fand model for the symmetric group n . When K is a field of characteristic zero and G = n , we give a finite dimensional K–subspace N of the polynomial ring K[x 1, …, x n ]. If K is the field of complex numbers, then N provides a Gel'fand model for G. The space N can be obtained as the zeros of certain differential operators (symmetrical operators) in the Weyl algebra.
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