arXiv subjects

Luis Enrique Ramírez

Publications and source records attributed to Luis Enrique Ramírez.

3 recordsLinked to original sources

arXiv2021

Faces of polyhedra associated with relation modules

Relation Gelfand-Tsetlin $\mathfrak{gl}_n$-modules were introduced in [FRZ19], and are determined by some special directed graphs and Gelfand-Tsetlin characters. In this work we constructed polyhedra associated with the class of relation modules, which includes as a particular case, any classical Gelfand-Tsetlin polytope. Following the ideas presented in [LM04] we give a characterization of $d$-faces of the associated polyhedra in terms of a matrix related to the corresponding graph.

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arXiv2018

Gelfand-Tsetlin Theory for Rational Galois Algebras

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 introduced in [PS09]. These polynomials are used to identify the action of the Gelfand-Tsetlin subalgebra on the BGG operators. We also provide explicit bases of the corresponding Gelfand-Tsetlin modules and prove a simplicity criterion for these modules. The results hold for modules defined over standard Galois orders of type $A$ - a large class of rings that include the universal enveloping algebra of $\mathfrak{gl} (n)$ and the finite $W$-algebras of type $A$.

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arXiv2017

Gelfand-Tsetlin modules over $\mathfrak{gl}(n,\mathbb C)$ with arbitrary characters

A Gelfand-Tsetlin tableau $T(v)$ induces a character $χ_v$ of the Gelfand-Tsetlin subalgebra $Γ$ of $U = U(\mathfrak{gl}(n,\mathbb C))$. By a theorem due to Ovsienko, for each tableau $T(v)$ there exists a finite number of nonisomorphic irreducible Gelfand-Tsetlin modules with $χ_v$ in its support, though explicit examples of such modules are only known for special families of characters. In this article we build a family of Gelfand-Tsetlin modules parametrized by characters, such that each character appears in its corresponding module. We also find the support of these modules, with multiplicities.

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