## 19 Citations

A study of Galois and flag orders

- Mathematics
- 2020

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

- MathematicsAsian 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

- Mathematics
- 2019

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

- Mathematics
- 2019

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

- Mathematics
- 2015

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

- MathematicsInternational 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

- Mathematics
- 2002

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…