Standard conjectures for the arithmetic Grassmannian G(2,N) and Racah polynomials
Andrew Kresch, Harry Tamvakis
Abstract
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 Plücker embedding of G in projective space. The analysis of the Hodge index inequalities involves estimates on certain Racah polynomials.
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