![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
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 Citation[8]). Gel'fand models for the linear group over a finite field can be found in Citation[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.