Annals of Global Analysis and Geometry· 2026Q2
Solving the index problem for (curved) Bernstein–Gelfand–Gelfand sequences
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- 2026year
Short summary
Researchers solved the index problem for curved Bernstein–Gelfand–Gelfand (BGG) sequences in parabolic geometry, demonstrating their fit into G-equivariant K-homology via Heisenberg calculus for flat parabolic geometries.
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Key points
- The index problem for curved BGG sequences in parabolic geometry is solved.
- A condition is provided for BGG sequences on flat parabolic geometry to fit into G-equivariant K-homology via Heisenberg calculus.
- A no-go theorem demonstrates the failure of this approach for higher rank Lie groups.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We study the index theory of curved Bernstein–Gelfand–Gelfand (BGG) sequences in parabolic geometry and their role in K -homology and noncommutative geometry. The BGG-sequences fit into K -homology, and we solve their index problem. We provide a condition for when the BGG-complex on the flat parabolic geometry G / P of a semisimple Lie group G fits into G -equivariant K -homology by means of Heisenberg calculus. For higher rank Lie groups, we prove a no-go theorem showing that the approach fails.
The authors' abstract, as published at the source. Annals of Global Analysis and Geometry, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics