Germán Benitez Monsalve

Federal University of Amazonas | UFAM · Department of Mathematics

Relation Gelfand–Tsetlin gln-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]...

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 presen...

Molev (in: Doebner, Scherer, Nattermann (eds) Group 21, physical applications and mathematical aspects of geometry, groups, and algebras, World Scientific, Singapore, vol 1, pp 172–176, 1997) constructed generators of the center of the universal enveloping algebra \(U(\mathfrak{g}_m(n))\) for the truncated current Lie algebra \(\mathfrak{g}_m(n) =...

Sergei Ovsienko proved that the Gelfand–Tsetlin variety for [Formula: see text] is equidimensional and the dimension of all irreducible components equals [Formula: see text]. This implies in particular the equidimensionality of the nilfiber of the (partial) Kostant–Wallach map. We generalize this result for the [Formula: see text]-partial Kostant–W...

S. Ovsienko proved that the Gelfand-Tsetlin variety for $\mathfrak{gl}_n$ is equidimensional (i.e., all its irreducible components have the same dimension) of dimension $\frac{n(n-1)}{2}$. This result is known as Ovsienko's Theorem and it has important consequences in Representation Theory of Algebras. In this paper, we will study the Gelfand-Tsetl...

S. Ovsienko proved that the Gelfand-Tsetlin variety for $\mathfrak{gl}_n$ is equidimensional (i.e. all its irreducible components have the same dimension) with dimension equals $\frac{n(n-1)}{2}$. This result has important consequences in Representation Theory of Algebras, implying, in particular, the equidimensionality of the fibers of the Kostant...