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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58923We 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 Plücker embedding of $G$ in projective space. The analysis of the Hodge index inequalities involves estimates on certain Racah polynomials.13 pages, LaTeX2eAlgebraic Geometry14G40; 14C17; 14M15; 33C45Standard conjectures for the arithmetic Grassmannian G(2,N) and Racah polynomialstext