Morphisms of Verma modules over exceptional Lie superalgebra E(5,10)

TL;DR

This paper investigates morphisms between Verma modules over the exceptional Lie superalgebra E(5,10), defining their degree and constructing morphisms of various degrees, ultimately classifying all degree 1 morphisms.

Contribution

It introduces a definition of morphism degree and constructs a series of morphisms over E(5,10), providing a complete classification of degree 1 morphisms.

Findings

All degree 1 morphisms are classified.

Constructed morphisms of various degrees.

Established a framework for morphism degrees in Lie superalgebras.

Abstract

In this paper we define the degree of a morphism between (generalized) Verma modules over a graded Lie superalgebra and construct series of morphisms of various degrees between (generalized) Verma modules over the exceptional infinite-dimensional linearly compact simple Lie superalgebra E(5,10). We prove that all such morphisms of degree 1 are found.