Special Values for Conformally Invariant Systems Associated to Maximal Parabolics of Quasi-Heisenberg Type

Systems of Differential Operators and Generalized Verma Modules

“…In [35], under the assumption that q is not of type D n (n − 2), we found the special values s 2 for Ω 2 systems for the Type 1a and Type 2 constituents. The technique that we used allowed us to handle each case uniformly.…”

“…A project for conformally invariant systems started with the work of [1] and [2]. Other progress on the project are reported in [18,19,20,21,22] and [33,34,35]. To see a recent development of the theory of conformally invariant systems the introduction of the work [22] of Kable is very helpful.…”

“…The present work is also part of the project. The aim of this paper is to close the cases that were left open in [35] and [34]. To describe our work of this paper more precisely, we now briefly review the works in the papers.…”

“…In [35], the parabolic subalgebra q = l ⊕ n was taken to be a maximal parabolic subalgebra of quasi-Heisenberg type, that is, a maximal parabolic subalgebra with nilpotent radical n with conditions that [n, [n, n]] = 0 and dim([n, n]) > 1. In this setting the Ω k systems for k ≥ 5 are zero.…”

“…To describe the open cases, let us now start explaining briefly the classification for the irreducible constituents W that contribute to Ω 2 systems. In [35], we first observed that if irreducible constituents W contribute to Ω 2 systems then their highest weights are of the form µ+ , where µ is the highest weight for g (1) and is some weight for g (1). We called such irreducible constituents special and classified as Type 1a, Type 1b, Type 2, and Type 3 with respect to certain technical conditions for the highest weight µ + .…”