Generalized Verma modules over sl(m+1) induced from simple highest weight modules

TL;DR

This paper constructs a class of generalized Verma modules over sl(m+1) from simple highest weight modules of gl(m), determines their simplicity criteria, and establishes an equivalence with tensor modules.

Contribution

It introduces a new class of generalized Verma modules over sl(m+1) and links them to tensor modules, providing clarity on their simplicity conditions.

Findings

Constructed generalized Verma modules from simple highest weight gl(m)-modules.

Determined simplicity criteria for these modules.

Established an equivalence with tensor modules.

Abstract

A class of generalized Verma modules over sl(m+1) are constructed from simple highest weight gl(m)-modules. Furthermore, the simplicity criterion for these sl(m+1)-modules are determined and an equivalence between generalized Verma modules and tensor modules are established.