# De Concini–Kac filtration and Gelfand–Tsetlin generators for quantum glN

@article{Futorny2019DeCF, title={De Concini–Kac filtration and Gelfand–Tsetlin generators for quantum glN}, author={Vyacheslav Futorny and Jonas Torbj{\"o}rn Hartwig}, journal={Linear Algebra and its Applications}, year={2019} }

## 3 Citations

Explicit construction of irreducible modules for U_q(gl_n)

- Mathematics
- 2017

We construct new families of U_q(gl_n)-modules by continuation from finite dimensional representations. Each such module is associated with a combinatorial object - admissible set of relations…

Explicit construction of irreducible modules for $$U_q(\mathfrak {gl}_n)$$Uq(gln)

- MathematicsSão Paulo Journal of Mathematical Sciences
- 2019

We construct new families of $$U_q(\mathfrak {gl}_n)$$Uq(gln)-modules by continuation from finite dimensional representations. Each such module is associated with a combinatorial object—admissible…

## References

SHOWING 1-10 OF 41 REFERENCES

Harish-Chandra Subalgebras and Gelfand-Zetlin Modules

- Mathematics
- 1994

A new framework for the study of some modules over algebras is elaborated and applied to a new class of representations of Lie algebra GL(n).

Harish-Chandra modules for Yangians

- Mathematics
- 2002

We study Harish-Chandra representations of Yangian for gl(2). We prove an analogue of Kostant theorem showing that resterited Yangians for gl(2) are free modules over certain maximal commutative…

On Gelfand-Zetlin modules over Uq(gln)

- Mathematics
- 2000

We construct and investigate a new large family of simple modules over Uq(gln).

A q-Analogue of the Centralizer Construction and Skew Representations of the Quantum Affine Algebra ?

- Mathematics
- 2006

We prove an analogue of the Sylvester theorem for the generator matrices of the quantum affine algebra Uq( b gln). We then use it to give an explicit realization of the skew representations of the…

Fibers of characters in Harish-Chandra categories

- Mathematics
- 2006

We solve the problem of extension of characters of commutative subalgebras in associative (noncommutative) algebras for a class of subrings (Galois orders) in skew group rings. These results can be…

Solution of a q-difference Noether problem and the quantum Gelfand-Kirillov conjecture for gl_N

- Mathematics
- 2011

It is shown that the q-difference Noether problem for all classical Weyl groups has a positive solution, simultaneously generalizing well known results on multisymmetric functions of Mattuck and…

Quantification de la Localisation de Dixmier de U(sln + 1(C))☆

- Mathematics
- 1999

Resume In this article, we extend to the quantum case the classical result of Dixmier, according to which, up to localization, the enveloping algebra of sln + 1(C) is a central polynomial extension…