On the homomorphisms between scalar generalized Verma modules

TL;DR

This paper investigates the structure of homomorphisms between scalar generalized Verma modules, proposing a conjecture that such homomorphisms are compositions of elementary ones, and confirms this for many cases with regular infinitesimal characters.

Contribution

The paper introduces a conjecture about the composition of homomorphisms between scalar generalized Verma modules and proves it for numerous parabolic subalgebras with regular infinitesimal characters.

Findings

Conjecture that all homomorphisms are compositions of elementary homomorphisms.

Confirmed the conjecture for many parabolic subalgebras with regular infinitesimal characters.

Provides new insights into the structure of scalar generalized Verma modules.

Abstract

We study the homomorphisms between scalar generalized Verma modules. We conjecture that any homomorphism between is composition of elementary homomorphisms. The purpose of this article is to show the conjecture is affirmative for many parabolic subalgebras under the assumption that the infinitesimal characters are regular.