First BGG operators via homogeneous examples
Jan Gregorovi\v{c}, Lenka Zalabov\'a
TL;DR
This paper explores first BGG operators within homogeneous geometries, providing new examples and methods to find solutions, thereby advancing understanding of parabolic geometries and their properties.
Contribution
It introduces novel approaches to solving first BGG operators on homogeneous geometries and presents new examples with interesting properties.
Findings
New solutions to first BGG operators on homogeneous geometries
Identification of new parabolic geometries admitting solutions
Enhanced understanding of properties and interpretations of these solutions
Abstract
We review the theory of first BGG operators and study how to approach them and find their solution on homogeneous geometries. We provide many new examples of parabolic geometries that admit solutions of first BGG operators with many interesting properties and interpretations.
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Taxonomy
TopicsAdvanced Topics in Algebra · Nonlinear Waves and Solitons · Algebraic and Geometric Analysis