A New family of simple $\mathfrak{gl}_{2n}(\mathbb{C})$-modules

Jonathan Nilsson

Vol. 283 (2016), No. 1, 1–19

DOI: 10.2140/pjm.2016.283.1

Abstract

We construct a new family of simple ${\mathfrak{g}\mathfrak{l}}_{2n}$-modules which depends on $n^2$ generic parameters. Each module in the family is isomorphic to the regular $U\left({\mathfrak{g}\mathfrak{l}}_n\right)$-module when restricted the ${\mathfrak{g}\mathfrak{l}}_n$-subalgebra naturally embedded into the top-left corner.

Keywords

Representation theory, Lie algebra, Nonweight module, Whittaker module

Mathematical Subject Classification 2010

Primary: 16G99

Milestones

Received: 14 September 2015

Accepted: 2 December 2015

Published: 14 June 2016