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arXiv · 1703.07264

A new way to construct 1-singular Gelfand-Tsetlin modules

Pablo Zadunaisky
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Abstract

We present a simplified way to construct the Gelfand-Tsetlin modules over $\mathfrak{gl}(n,\mathbb C)$ related to a $1$-singular GT-tableau defined by Futorny, Grantcharov and Ramirez. We begin by reframing the classical construction of generic Gelfand-Tsetlin modules found by Drozd, Futorny and Ovsienki, showing that they form a flat family over generic points of $\mathbb C^{\binom{n}{2}}$. We then show that this family can be extended to a flat family over a variety including generic points and $1$-singular points for a fixed singular pair of entries. The $1$-singular modules are precisely the fibers over these points.

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Pablo Zadunaisky. 2017-03-21. A new way to construct 1-singular Gelfand-Tsetlin modules. https://arxiv.org/abs/1703.07264

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