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Algebra and Discrete Mathematics, 2017, Volume 23, Issue 1, Pages 180–193 (Mi adm599)  

This article is cited in 11 scientific papers (total in 11 papers)

RESEARCH ARTICLE

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

Pablo Zadunaisky

Instituto de Matemática e Estatística, Universidade de São Paulo, São Paulo SP, Brasil
References:
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 in [6]. We begin by reframing the classical construction of generic Gelfand-Tsetlin modules found in [3], 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.
Keywords: Gelfand-Tsetlin modules, Gelfand-Tsetlin bases, tableaux realization.
Funding agency Grant number
Fundação de Amparo à Pesquisa do Estado de São Paulo 2016-25984-1
The author is a FAPESP PostDoc Fellow, grant 2016-25984-1.
Received: 21.03.2017
Revised: 30.03.2017
Bibliographic databases:
Document Type: Article
MSC: 17B10
Language: English
Citation: Pablo Zadunaisky, “A new way to construct $1$-singular Gelfand-Tsetlin modules”, Algebra Discrete Math., 23:1 (2017), 180–193
Citation in format AMSBIB
\Bibitem{Zad17}
\by Pablo~Zadunaisky
\paper A new way to construct $1$-singular Gelfand-Tsetlin modules
\jour Algebra Discrete Math.
\yr 2017
\vol 23
\issue 1
\pages 180--193
\mathnet{http://mi.mathnet.ru/adm599}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000398979400009}
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  • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Algebra and Discrete Mathematics
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