A new way to construct \(1\)-singular Gelfand-Tsetlin modules
We present a simplified way to construct the Gelfand-Tsetlin modules over$\gl(n,\CC)$ related to a $1$-singular GT-tableau defined in\cite{FGR-singular-gt}. We begin by reframing the classical construction ofgeneric Gelfand-Tsetlin modules found in~\cite{DFO-GT-modules}, showingthat they form a flat...
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| Date: | 2017 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Lugansk National Taras Shevchenko University
2017
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| Subjects: | |
| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/444 |
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| Journal Title: | Algebra and Discrete Mathematics |
Institution
Algebra and Discrete Mathematics| Summary: | We present a simplified way to construct the Gelfand-Tsetlin modules over$\gl(n,\CC)$ related to a $1$-singular GT-tableau defined in\cite{FGR-singular-gt}. We begin by reframing the classical construction ofgeneric Gelfand-Tsetlin modules found in~\cite{DFO-GT-modules}, showingthat they form a flat family over generic points of $\CC^{\binom{n}{2}}$. Wethen show that this family can be extended to a flat family over a varietyincluding generic points and $1$-singular points for a fixed singular pairof entries. The $1$-singular modules are precisely the fibers over thesepoints. |
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