Proceedings of the Japan Academy, Series A, Mathematical Sciences

Conformally invariant systems of differential operators associated to maximal parabolics of quasi-Heisenberg type

Toshihisa Kubo

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Abstract

Let $G_{0}$ be a simple Lie group and $Q_{0}$ a maximal parabolic subgroup of quasi-Heisenberg type. In this paper we construct conformally invariant systems of differential operators associated to a homogeneous line bundle $\mathcal{L}_{s} \to G_{0}/Q_{0}$. The systems that we construct yield explicit homomorphisms between appropriate generalized Verma modules. We also determine whether or not these homomorphisms are standard.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 89, Number 3 (2013), 41-46.

Dates
First available in Project Euclid: 1 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.pja/1362146477

Digital Object Identifier
doi:10.3792/pjaa.89.41

Mathematical Reviews number (MathSciNet)
MR3032084

Zentralblatt MATH identifier
1277.22013

Subjects
Primary: 22E46: Semisimple Lie groups and their representations
Secondary: 17B10: Representations, algebraic theory (weights) 22E47: Representations of Lie and real algebraic groups: algebraic methods (Verma modules, etc.) [See also 17B10]

Keywords
Intertwining differential operator generalized Verma module real flag manifold

Citation

Kubo, Toshihisa. Conformally invariant systems of differential operators associated to maximal parabolics of quasi-Heisenberg type. Proc. Japan Acad. Ser. A Math. Sci. 89 (2013), no. 3, 41--46. doi:10.3792/pjaa.89.41. https://projecteuclid.org/euclid.pja/1362146477


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