论文标题
$ \ mathfrak {sl}（n+1）$的张量模块的启动和傅立叶变换
Exponentiation and Fourier transform of tensor modules of $\mathfrak{sl} (n+1)$
论文作者
论文摘要
借助启动器和傅立叶变换，我们引入了一类模块$ t（g，v，s）$ $ \ mathfrak {sl}（n+1）$的混合张量型。通过改变多项式$ g $，$ \ mathfrak {gl}（n）$ - 模块$ v $和set $ s $，我们在cartan subalgebra $ \ mathfrak H $ of $ \ mathfrak {sl}（sl+1）$，和$ $ $ $ $ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ \ $ h $ h $ h $ of cartan subalgebra $ \ mathfrak h $上获得重要类别的重量模块。此外，这些模块是通过在差分运算符方面明确表示$ \ mathfrak {sl}（n+1）$的元素获得的，并导致新的张量相干家庭的$ \ mathfrak {sl}}（sl sl}（n+1）$。提供了$ t（g，v，s）$的同构定理和简单标准。
With the aid of the exponentiation functor and Fourier transform we introduce a class of modules $T(g,V,S)$ of $\mathfrak{sl} (n+1)$ of mixed tensor type. By varying the polynomial $g$, the $\mathfrak{gl}(n)$-module $V$, and the set $S$, we obtain important classes of weight modules over the Cartan subalgebra $\mathfrak h$ of $\mathfrak{sl} (n+1)$, and modules that are free over $\mathfrak h$. Furthermore, these modules are obtained through explicit presentation of the elements of $\mathfrak{sl} (n+1)$ in terms of differential operators and lead to new tensor coherent families of $\mathfrak{sl} (n+1)$. An isomorphism theorem and simplicity criterion for $T(g,V,S)$ is provided.
