Irreducible Generic Gelfand-Tsetlin Modules of $\mathfrak{gl}(n)$

TL;DR

This paper classifies and constructs explicit bases for all irreducible generic Gelfand-Tsetlin modules of the Lie algebra rak{gl}(n), advancing the understanding of their structure.

Contribution

It provides a complete classification and explicit basis construction for all irreducible generic Gelfand-Tsetlin modules of rak{gl}(n), which was previously unknown.

Findings

Complete classification of irreducible generic Gelfand-Tsetlin modules.

Explicit bases constructed for these modules.

Enhanced understanding of rak{gl}(n) representation theory.

Abstract

We provide a classification and explicit bases of tableaux of all irreducible generic Gelfand-Tsetlin modules for the Lie algebra $\mathfrak{gl}(n)$.