Glider representations of chains of semisimple Lie algebras

Abstract

We start the study of glider representations in the setting of semisimple Lie algebras. A glider representation is defined for some positively filtered ring $FR$ and here we consider the right bounded algebra filtration $FU(\mathfrak{g})$ on the universal enveloping algebra $U(\mathfrak{g})$ of some semisimple Lie algebra $\mathfrak{g}$ given by a fixed chain of semisimple sub Lie algebras ${\mathfrak{g}}_1\subset {\mathfrak{g}}_2\subset \dots \subset {\mathfrak{g}}_n=\mathfrak{g}$. Inspired by the classical representation theory, we introduce so-called Verma glider representations. Their existence is related to the relations between the root systems of the appearing Lie algebras ${\mathfrak{g}}_i$. In particular, we consider chains of simple Lie algebras of the same type $A,B,C$ and $D$.

24 pages

References in corpus (1)

• Localization and sheaves of glider representations