Standard conjectures for the arithmetic Grassmannian G(2,N) and Racah polynomials

摘要

We prove the arithmetic Hodge index and hard Lefschetz conjectures for the Grassmannian G = G (2, N) parametrizing lines in projective space, for the natural arithmetic Lefschetz: operator defined via the Plucker embedding of G in projective space. The analysis of the Hodge index inequality involves estimates on values of certain Racah polynomials. [References: 25]