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.
