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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| Дата: | 2017 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2017
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/444 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-4442017-04-10T07:40:45Z A new way to construct \(1\)-singular Gelfand-Tsetlin modules Zadunaisky, Pablo Gelfand-Tsetlin modules, Gelfand-Tsetlin bases, tableaux realization 17B10 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. Lugansk National Taras Shevchenko University 2017-04-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/444 Algebra and Discrete Mathematics; Vol 23, No 1 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/444/95 Copyright (c) 2017 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
Gelfand-Tsetlin modules Gelfand-Tsetlin bases tableaux realization 17B10 |
| spellingShingle |
Gelfand-Tsetlin modules Gelfand-Tsetlin bases tableaux realization 17B10 Zadunaisky, Pablo A new way to construct \(1\)-singular Gelfand-Tsetlin modules |
| topic_facet |
Gelfand-Tsetlin modules Gelfand-Tsetlin bases tableaux realization 17B10 |
| format |
Article |
| author |
Zadunaisky, Pablo |
| author_facet |
Zadunaisky, Pablo |
| author_sort |
Zadunaisky, Pablo |
| title |
A new way to construct \(1\)-singular Gelfand-Tsetlin modules |
| title_short |
A new way to construct \(1\)-singular Gelfand-Tsetlin modules |
| title_full |
A new way to construct \(1\)-singular Gelfand-Tsetlin modules |
| title_fullStr |
A new way to construct \(1\)-singular Gelfand-Tsetlin modules |
| title_full_unstemmed |
A new way to construct \(1\)-singular Gelfand-Tsetlin modules |
| title_sort |
new way to construct \(1\)-singular gelfand-tsetlin modules |
| description |
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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2017 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/444 |
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AT zadunaiskypablo anewwaytoconstruct1singulargelfandtsetlinmodules AT zadunaiskypablo newwaytoconstruct1singulargelfandtsetlinmodules |
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2024-04-12T06:26:11Z |
| last_indexed |
2024-04-12T06:26:11Z |
| _version_ |
1796109156224073728 |