Homomorphisms between scalar Vema modules of ${\mathfrak gl}(n, {\mathbb C})$

TL;DR

This paper classifies all homomorphisms between scalar generalized Verma modules of gl(n,C), showing they are compositions of elementary homomorphisms, thus providing a complete structural understanding.

Contribution

It provides a complete classification of homomorphisms between scalar generalized Verma modules of gl(n,C), revealing they are compositions of elementary homomorphisms.

Findings

Homomorphisms are compositions of elementary homomorphisms.

Complete classification of scalar generalized Verma module homomorphisms.

Structural insight into module homomorphisms in Lie algebra representation theory.

Abstract

In this article, we classify the homomorphisms between scalar generalized Verma modules of ${\mathfrak gl}(n, {\mathbb C})$. In fact such homomorphisms are compositions of elementary homomorphisms.