Solving the index problem for (curved) BernsteinGelfandGelfand sequences
Abstract
We study the index theory of curved BernsteinGelfandGelfand (BGG) sequences in parabolic geometry and their role in $K$homology and noncommutative geometry. The BGGsequences fit into $K$homology, and we solve their index problem. We provide a condition for when the BGGcomplex 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 nogo theorem showing that the approach fails.
 Publication:

arXiv eprints
 Pub Date:
 June 2024
 DOI:
 10.48550/arXiv.2406.07033
 arXiv:
 arXiv:2406.07033
 Bibcode:
 2024arXiv240607033G
 Keywords:

 Mathematics  KTheory and Homology;
 Mathematics  Differential Geometry;
 Mathematics  Operator Algebras;
 Mathematics  Representation Theory
 EPrint:
 33 pages