On the homomorphisms between the generalized Verma modules arising from conformally invariant systems

TL;DR

This paper investigates the nature of homomorphisms between generalized Verma modules generated by conformally invariant differential operators, focusing on their standard or non-standard classification for specific parabolic subalgebras.

Contribution

It determines whether homomorphisms from first and second order conformally invariant differential operators are standard or non-standard in the context of maximal parabolic subalgebras of quasi-Heisenberg type.

Findings

Homomorphisms from certain differential operators are identified as standard or non-standard.

The classification depends on the order of the differential operators and the structure of the parabolic subalgebra.

Provides explicit criteria for the standardness of these homomorphisms.

Abstract

It is shown by Barchini, Kable, and Zierau that conformally invariant systems of differential operators yield explicit homomorphisms between certain generalized Verma modules. In this paper we determine whether or not the homomorphisms arising from such systems of first and second order differential operators associated to maximal parabolic subalgebras of quasi-Heisenberg type are standard.