A new way to construct 1-singular Gelfand-Tsetlin modules

Abstract

We present a simplified way to construct the Gelfand-Tsetlin modules over gl(n,C) related to a 1-singular GT-tableau defined by Futorny, Grantcharov and Ramirez. We begin by reframing the classical construction of generic Gelfand-Tsetlin modules found by Drozd, Futorny and Ovsienki, showing that they form a flat family over generic points of C^{n choose 2}. We then show that this family can be extended to a flat family over a variety including generic points and 1-singular points for a fixed singular pair of entries. The 1-singular modules are precisely the fibers over these points.