论文标题
标准标志和主要旗帜订单之间的地图
Maps between standard and principal flag orders
论文作者
论文摘要
Galois订单由V. Futorny和S. Ovsienko于2010年推出，形成了一类关联代数，其中包含许多重要示例，例如$ \ mathfrak {gl} _n $的包裹代数（以及其量子变形），量子变形及其量子变形），概括的weyl代数代数和转移的Yangians和移位。引入Galois订单的主要动机是为研究某些无限尺寸不可减至的表示提供设置，称为Gelfand-Tsetlin模块。 J. Hartwig在2017年定义的主要Galois订单是具有额外财产的Galois订单，这使其更容易学习。所有提到的例子是主要的galois命令。 2019年，B。Webster定义了主要的标志订单，在大多数情况下，这与主要的Galois命令相当，并进一步简化了他们的研究。本文介绍了一些将标准标志和GALOIS订单的研究对与相关数据联系起来的技术。这样的技术包括：标准标志和加洛伊斯订单之间存在形态的足够条件，与仿射品种差异操作员有关的标志订单的属性，以及构建标准和主要旗帜和galois订单的张量产品。
Galois orders, introduced in 2010 by V. Futorny and S. Ovsienko, form a class of associative algebras that contain many important examples, such as the enveloping algebra of $\mathfrak{gl}_n$ (as well as its quantum deformation), generalized Weyl algebras, and shifted Yangians. The main motivation for introducing Galois orders is they provide a setting for studying certain infinite dimensional irreducible representations, called Gelfand-Tsetlin modules. Principal Galois orders, defined by J. Hartwig in 2017, are Galois orders with an extra property, which makes them easier to study. All of the mentioned examples are principal Galois orders. In 2019, B. Webster defined principal flag orders which in most situations are Morita equivalent to principal Galois orders, and further simplifies their study. This paper describes some techniques to connect the study pairs of standard flag and Galois orders with related data. Such techniques include: a sufficient condition for morphisms between standard flag and Galois orders to exist, a property of flag orders related to differential operators on affine varieties, and constructing tensor products of standard and principal flag and Galois orders.
