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Gelfand-Tsetlin theory for rational Galois algebras
Israel Journal of Mathematics ( IF 0.8 ) Pub Date : 2020-08-01 , DOI: 10.1007/s11856-020-2048-2
Vyacheslav Futorny , Dimitar Grantcharov , Luis Enrique Ramirez , Pablo Zadunaisky

In the present paper we study Gelfand-Tsetlin modules defined in terms of BGG differential operators. The structure of these modules is described with the aid of the Postnikov-Stanley polynomials introduced in [PS09]. These polynomials are used to identify the action of the Gelfand-Tsetlin subalgebra on the BGG operators. We also provide explicit bases of the corresponding Gelfand-Tsetlin modules and prove a simplicity criterion for these modules. The results hold for modules defined over standard Galois orders of type $A$ - a large class of rings that include the universal enveloping algebra of $\mathfrak{gl} (n)$ and the finite $W$-algebras of type $A$.

中文翻译:

有理伽罗瓦代数的 Gelfand-Tsetlin 理论

在本文中,我们研究了根据 BGG 微分算子定义的 Gelfand-Tsetlin 模块。这些模块的结构借助 [PS09] 中介绍的 Postnikov-Stanley 多项式进行了描述。这些多项式用于识别 Gelfand-Tsetlin 子代数对 BGG 算子的作用。我们还提供了相应 Gelfand-Tsetlin 模块的明确基础,并证明了这些模块的简单性标准。结果适用于定义在 $A$ 类型的标准 Galois 阶上的模块 - 一大类环,包括 $\mathfrak{gl} (n)$ 的通用包络代数和 $A 类型的有限 $W$-代数$.
更新日期:2020-08-01
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