Gelfand-Tsetlin variety for $\mathfrak{gl}_n$

Germán Benitez Monsalve

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arXiv · 1802.07248

Gelfand-Tsetlin variety for $\mathfrak{gl}_n$

Germán Benitez Monsalve

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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) 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 nilfiber of the Kostant-Wallach map. In this paper we will present the generalization of this result and will address a weak version of Ovsienko's Theorem which includes the regular case.

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BibTeX RIS

Germán Benitez Monsalve. 2018-02-20. Gelfand-Tsetlin variety for $\mathfrak{gl}_n$. https://arxiv.org/abs/1802.07248

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