Conference abstracts

Session S08 - Lie Groups and Representations

No date set

## Equidimensionality of some Gelfand-Tsetlin varieties

### Instituto de Matemática e Estatística (IME) / Universidade de São Paulo (USP), Brazil   -   gabm03@gmail.com

S. Ovsienko proved in $2003$ that the Gelfand-Tsetlin variety for $gl(n)$ is equidimensional, i.e., all its irreducible components had the same dimension, in that case, such dimension is the dimension of affine space minus the number of equations. This result allows:

1. It guarantees the existence of irreducible modules in $gl(n)$ which are parameterized by the maximal espectrum of the Gelfand-Tsetlin subalgebra for $gl(n)$.

2. The universal enveloping algebra of $gl(n)$ is free as left and right module over its Gelfand-Tsetlin subalgebra.

In this poster, we will show the Gelfand-Tsetlin variety for $gl(n)$, the version for the quantum group Restricted Yangian of gl(n) and its equidimesionality.