Exponentiation and Fourier transform of tensor modules of sl(n+1)

Abstract

With the aid of the exponentiation functor and Fourier transform we introduce a class of modules T ( g , V , S ) of sl ( n + 1 ) of mixed tensor type. By varying the polynomial g , the gl ( n ) -module V , and the set S , we obtain important classes of weight modules over the Cartan subalgebra h of sl ( n + 1 ) , and modules that are free over h . Furthermore, these modules are obtained through explicit presentation of the elements of sl ( n + 1 ) in terms of differential operators and lead to new tensor coherent families of sl ( n + 1 ) . An isomorphism theorem and a simplicity criterion for T ( g , V , S ) is provided.