Gelfand-Tsetlin varieties for Yangians
Germ\'an Benitez Monsalve

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 is equidimensional (i.e., all its irreducible components have the same dimension) of dimension . 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 and the equidimensionality for .
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic structures and combinatorial models · Advanced Topics in Algebra
