The Hard Lefschetz Theorem in positive characteristic for the Flag Varieties

TL;DR

This paper characterizes primes in positive characteristic for which the Hard Lefschetz Theorem applies to flag varieties, identifying specific conditions on weights and cohomology.

Contribution

It provides a criterion for when the Hard Lefschetz Theorem holds in positive characteristic for flag varieties based on primes and weights.

Findings

Identifies primes p where the theorem holds

Characterizes weights λ for the theorem's validity

Connects cohomology properties with prime characteristics

Abstract

For a given flag variety, we characterize the primes $p$ for which there exists a weight $\lambda$ such that the Hard Lefschetz Theorem holds for multiplication by $\lambda$ on the cohomology of the flag variety with coefficients in an infinite field of characteristic $p$.