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 in [6]. We begin by reframing the classical construc- tion of generic Gelfand-Tsetlin modules found in [3], showing that

they form a flat family over generic points of C( n 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.