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Journal of Lie Theory 23 (2013), No. 3, 847--883
Copyright Heldermann Verlag 2013

On the Homomorphisms between the Generalized Verma Modules Arising from Conformally Invariant Systems

Toshihisa Kubo
Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan

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.

Keywords: Conformally invariant systems, intertwining differential operators, generalized Verma modules, standard maps.

MSC: 22E47; 17B10

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