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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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