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

2017/03/21 by Zadunaisky, Pablo · 1 citation
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1703.07264

Abstract

We present a simplified way to construct the Gelfand-Tsetlin modules over \mathfrakgl(n,\mathbb 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 \mathbb C^\binomn2. 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.

Cited by

• Simple subquotients of relation modules

Related

• Singular Gelfand-Tsetlin modules of \mathfrakgl(n)
• Geometric approach to p-singular Gelfand-Tsetlin \mathfrak gl_n-modules
• A geometric approach to 1-singular Gelfand-Tsetlin \mathfrak gl_n-modules
• Gelfand-Tsetlin modules over mathfrakgl(n, mathbb C) with arbitrary\n characters
• Families of irreducible singular Gelfand-Tsetlin modules of \mathfrakgl(n)