A system of third-order differential operators conformally invariant under sl(3, ℂ) and so(8, ℂ)

Toshihisa Kubo

Vol. 253 (2011), No. 2, 439–453

DOI: 10.2140/pjm.2011.253.439

Abstract

Barchini, Kable, and Zierau constructed a number of conformally invariant systems of differential operators associated to Heisenberg parabolic subalgebras in simple Lie algebras. The construction was systematic, but the existence of such a system was left open in two cases, namely, the Ω₃ system for type A₂ and type D₄. Here, such a system is shown to exist for both cases. The construction of the system may also be interpreted as giving an explicit homomorphism between generalized Verma modules.

Keywords

intertwining differential operator, generalized Verma module, real flag manifold

Mathematical Subject Classification 2010

Primary: 22E46

Secondary: 17B10, 22E47

Milestones

Received: 26 September 2010

Revised: 30 March 2011

Accepted: 29 April 2011

Published: 21 January 2012