Igor Souza do Nascimento (Universidade Federal do Amazonas)
For every n greater or equal to 1, the Gelfand-Tsetlin subalgebra of gl(n) is a finitely generated subalgebra of it's enveloping algebra U(gl(n)). By the Poincaré-Birkhoff-Witt Theorem, we can identify U(gl(n)) with the ring of polinomyals in n times n variables, and by doing so, we can see the Gelfand-Tsetlin subalgebra as an algebra of polynomials. Associating it to a variety, we prove that it is equidimensional, in the sense that every irreducible component have the same dimension; with this affirmative answer, many results arise in the representation theory of associative algebras and Lie algebras. The goal of this poster is to briefly explain this results and it's consequences in the representation theory.