Gelfand-Tsetlin varieties for Yangians

TL;DR

This paper extends the study of Gelfand-Tsetlin varieties to restricted Yangians, proving equidimensionality results for specific cases, which has implications in the representation theory of these algebraic structures.

Contribution

It introduces the analysis of Gelfand-Tsetlin varieties for restricted Yangians and establishes equidimensionality for the case of $Y_p(\mathfrak{gl}_3)$, expanding known results.

Findings

Gelfand-Tsetlin variety for $Y_p(\mathfrak{gl}_n)$ studied

Proves equidimensionality for $Y_p(\mathfrak{gl}_3)$

Connects results to representation theory of Yangians

Abstract

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-Tsetlin varieties for restricted Yangian $Y_p(\mathfrak{gl}_n)$ and the equidimensionality for $Y_p(\mathfrak{gl}_3)$.