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arXiv · 1606.03394

New singular Gelfand-Tsetlin $\mathfrak{gl} (n)$-modules of index 2

Vyacheslav Futorny·Dimitar Grantcharov·Luis Enrique Ramirez
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Abstract

Singular Gelfand-Tsetlin modules of index 2 are modules whose tableaux bases may have singular pairs but no singular triples of entries on each row. In this paper we construct singular Gelfand-Tsetlin modules for arbitrary singular character of index 2. Explicit bases of derivative tableaux and the action of the generators of $\mathfrak{gl}(n)$ are given for these modules. Our construction leads to new families of irreducible Gelfand-Tsetlin modules and also provides tableaux bases for some simple Verma modules.

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BibTeXRIS

Vyacheslav Futorny, Dimitar Grantcharov, Luis Enrique Ramirez. 2017-06-15. New singular Gelfand-Tsetlin $\mathfrak{gl} (n)$-modules of index 2. https://doi.org/10.1007/s00220-017-2967-x

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