Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 008, 35 pages      arXiv:1304.1646      https://doi.org/10.3842/SIGMA.2014.008

Systems of Differential Operators and Generalized Verma Modules

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

Received April 08, 2013, in final form January 17, 2014; Published online January 24, 2014

Abstract
In this paper we close the cases that were left open in our earlier works on the study of conformally invariant systems of second-order differential operators for degenerate principal series. More precisely, for these cases, we find the special values of the systems of differential operators, and determine the standardness of the homomorphisms between the generalized Verma modules, that come from the conformally invariant systems.

Key words: conformally invariant systems; quasi-invariant differential operators; intertwining differential operators; real flag manifolds; generalized Verma modules; standard maps.

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