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Galois orders, introduced in 2010 by V. Futorny and S. Ovsienko, form a classof associative algebras that contain many important examples, such as theenveloping algebra of $\mathfrak{gl}_n$ (as well as its quantum deformation),generalized Weyl algebras, and shifted Yangians. The main motivation forintroducing Galois orders is they provide a setting for studying certaininfinite dimensional irreducible representations, called Gelfand-Tsetlinmodules. Principal Galois orders, defined by J. Hartwig in 2017, are Galoisorders with an extra property, which makes them easier to study. All of thementioned examples are principal Galois orders. In 2019, B. Webster definedprincipal flag orders which in most situations are Morita equivalent toprincipal Galois orders and further simplifies their study. This paperdescribes some techniques to connect the study pairs of standard flag andGalois orders with data. Such techniques include: a sufficient condition formorphisms between standard flag and Galois orders to exist, a property of flagorders related to differential operators on affine varieties, and constructingtensor products of standard and principal flag and Galois orders.

Maps between standard and principal flag orders