Singular BGG complexes for the symplectic case
Rafael Mr{\dj}en
TL;DR
This paper constructs singular BGG complexes for the symplectic case using the Penrose transform, demonstrating their exactness over the big affine cell in a holomorphic geometric setting.
Contribution
It introduces a novel method to build singular BGG complexes in the symplectic case via the Penrose transform, extending previous resolutions to singular infinitesimal characters.
Findings
Constructed singular BGG complexes for the symplectic case.
Proved the complexes are exact over the big affine cell.
Extended BGG resolutions to singular infinitesimal characters.
Abstract
Using the Penrose transform, we construct analogues of the BGG (Bernstein-Gelfand-Gelfand) resolutions in certain singular infinitesimal characters, in the holomorphic geometric setting, over the Lagrangian Grassmannian. We prove the exactness of the constructed complex over the big affine cell.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAdvanced Algebra and Geometry · Nonlinear Waves and Solitons · Algebraic structures and combinatorial models