Abstract

AbstractWe prove an analogue of Koszul duality for category$ \mathcal{O} $of a reductive group$G$in positive characteristic$\ell $larger than$1$plus the number of roots of$G$. However, there are no Koszul rings, and we do not prove an analogue of the Kazhdan–Lusztig conjectures in this context. The main technical result is the formality of the dg-algebra of extensions of parity sheaves on the flag variety if the characteristic of the coefficients is at least the number of roots of$G$plus$2$.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.