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arXiv · 1705.05793

Geometric approach to $p$-singular Gelfand-Tsetlin $\mathfrak {gl}_n$-modules

Elizaveta Vishnyakova
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Abstract

We give an elementary construction of a $p\geq 1$-singular Gelfand-Tsetlin $\mathfrak{gl}_n(\mathbb C)$-module in terms of local distributions. This is a generalization of the universal $1$-singular Gelfand-Tsetlin $\mathfrak{gl}_n(\mathbb C)$-module obtained in [FGR1]. We expect that the family of new Gelfand-Tsetlin modules that we obtained will lead to a classification of all irreducible $p>1$-singular Gelfand-Tsetlin modules. So far such a classification is known only for singularity $n=1$.

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BibTeXRIS

Elizaveta Vishnyakova. 2017-05-16. Geometric approach to $p$-singular Gelfand-Tsetlin $\mathfrak {gl}_n$-modules. https://arxiv.org/abs/1705.05793

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