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

Abstract

We give an elementary construction of a $p\ge 1$-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 $n=1$.

arXiv comment11 pages

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