# Principal Galois orders and Gelfand-Zeitlin modules

@article{Hartwig2017PrincipalGO,
title={Principal Galois orders and Gelfand-Zeitlin modules},
author={Jonas Torbj{\"o}rn Hartwig},
journal={arXiv: Representation Theory},
year={2017}
}
• J. Hartwig
• Published 11 October 2017
• Mathematics
• arXiv: Representation Theory
A study of Galois and flag orders
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 gln (as well as its
Harish–Chandra modules over invariant subalgebras in a skew-group ring
• Mathematics
Asian Journal of Mathematics
• 2021
We construct a new class of algebras resembling enveloping algebras and generalizing orthogonal Gelfand-Zeitlin algebras and rational Galois algebras studied by [EMV,FuZ,RZ,Har]. The algebras are
Gelfand-Tsetlin modules in the Coulomb context
This paper gives a new perspective on the theory of principal Galois orders as developed by Futorny, Ovsienko, Hartwig and others. Every principal Galois order can be written as $eFe$ for any
Gelfand-Tsetlin theory for rational Galois algebras
• Mathematics
• 2018
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
Gelfand-Tsetlin modules: canonicity and calculations.
• Mathematics
• 2020
In this paper, we give a more down-to-earth introduction to the connection between Gelfand-Tsetlin modules over $\mathfrak{gl}_n$ and diagrammatic KLRW algebras, and develop some of its consequences.
An Alternating Analogue of $U(\mathfrak{gl}_n)$ and its Representations
In 2010, V. Futorny and S. Ovsienko gave a realization of $U(\mathfrak{gl}_n)$ as a subalgebra of the ring of invariants of a certain noncommutative ring with respect to the action of $S_1\times On rational twisted generalized Weyl algebra • Mathematics • 2020 The aim of this work is to investigate the structure of some skew twisted algebras, when the coefficient ring is a localization of the polynomial ring over the field of characteristic zero, and an ## References SHOWING 1-10 OF 39 REFERENCES Fibers of characters in Gelfand-Tsetlin categories • Mathematics • 2014 For a class of noncommutative rings, called Galois orders, we study the problem of an extension of characters from a commutative subalgebra. We show that for Galois orders this problem is always The q-difference Noether problem for complex reflection groups and quantum OGZ algebras ABSTRACT For any complex reflection group G = G(m,p,n), we prove that the G-invariants of the division ring of fractions of the n:th tensor power of the quantum plane is a quantum Weyl field and give Canonical Gelfand–Zeitlin Modules over Orthogonal Gelfand–Zeitlin Algebras • Mathematics International Mathematics Research Notices • 2019 We prove that every orthogonal Gelfand–Zeitlin algebra$U$acts (faithfully) on its Gelfand–Zeitlin subalgebra$\Gamma \$. Considering the dual module, we show that every Gelfand–Zeitlin character
Special transverse slices and their enveloping algebras
Let G be a simple, simply connected algebraic group over Image, Image=Lie G, Image (Image) the nilpotent cone of Image, and (E,H,F) an ImageImage2-triple in Image. Let S=E+Ker ad F, the special
Gelfand-Zeitlin Theory from the Perspective of Classical Mechanics. II
• Mathematics
• 2006
Let M(n) be the algebra (both Lie and associative) of n × n matrices over ℂ. Then M(n) inherits a Poisson structure from its dual using the bilinear form (x, y) = −tr xy. The Gl(n) adjoint orbits are