Schubert Calculus on the Arithmetic Grassmannian
نویسنده
چکیده
Let G be the arithmetic Grassmannian over SpecZ with the natural invariant Kähler metric on G(C). We study the combinatorics of the arithmetic Schubert calculus in the Arakelov Chow ring CH(G). We obtain formulas for the arithmetic Littlewood-Richardson numbers and the Faltings height of G under the Plücker embedding, using ‘rim hook operations’ on Young diagrams. An analysis of the duality involution leads to new combinatorial relations among Kostka numbers.
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تاریخ انتشار 1999