Constructing p, n-forms from p-forms via the Hodge star operator and the exterior derivative

. A G ] 2 9 Ju n 20 03 THE HODGE STAR OPERATOR ON SCHUBERT FORMS

Let X = G/P be a homogeneous space of a complex semisimple Lie group G equipped with a hermitian metric. We study the action of the Hodge star operator on the space of harmonic differential forms on X. We obtain explicit combinatorial formulas for this action when X is an irreducible hermitian symmetric space of compact type.

The Harmonic Operator for Exterior Differential Forms.

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We consider the p-adic Galois representation associated to a Hilbert modular form. Carayol has shown that, under a certain assumption, its restriction to the local Galois group at a place not dividing p is compatible with the local Langlands correspondence [C2]. In this paper, we show that the same is true for the places dividing p, in the sense of p-adic Hodge theory [Fo], as is shown for an e...

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Resultants and Chow Forms via Exterior Syzygies

Let W be a vector space of dimension n+ 1 over a field K. The Chow divisor of a k-dimensional variety X in P = P(W ) is the hypersurface, in the Grassmannian Gk+1 of planes of codimension k+1 in P, whose points (over the algebraic closure of K) are the planes that meet X . The Chow form of X is the defining equation of the Chow divisor. For example, the resultant of k+ 1 forms of degree e in k ...