# Low degree morphisms of E(5,10)-generalized verma modules

## TL;DR

This paper investigates morphisms of low degree between generalized Verma modules over the exceptional Lie superalgebra E(5,10), classifying these morphisms and confirming a conjecture by Rudakov.

## Contribution

It provides a classification of low-degree morphisms between Verma modules over E(5,10) and proves Rudakov's conjecture in these cases.

## Key findings

- Classified degree one, two, and three morphisms between Verma modules.
- Confirmed Rudakov's conjecture for these morphism degrees.
- Developed a combinatorial description of module restrictions.

## Abstract

In this paper we face the study of the representations of the exceptional Lie superalgebra E(5,10). We recall the construction of generalized Verma modules and give a combinatorial description of the restriction to sl_5 of the Verma module induced by the trivial representation. We use this description to classify morphisms between Verma modules of degree one, two and three proving in these cases a conjecture given by Rudakov. A key tool is the notion of dual morphism between Verma modules.