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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Communicated by Y. Kawahigashi
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Futorny, V., Grantcharov, D. & Ramirez, L.E. New Singular Gelfand–Tsetlin \({\mathfrak{gl}(n)}\)-Modules of Index 2. Commun. Math. Phys. 355, 1209–1241 (2017). https://doi.org/10.1007/s00220-017-2967-x
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DOI: https://doi.org/10.1007/s00220-017-2967-x