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The Jordan-Hoelder series for nearby cycles on some Shimura varieties and affine flag varieties

Ulrich Goertz·Thomas J. Haines
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Abstract

We study the Jordan-Hoelder series for nearby cycles on certain Shimura varieties and Rapoport-Zink local models, and on finite-dimensional pieces of Beilinson's deformation of the affine Grassmannian to the affine flag variety (and their p-adic analogues). We give a formula for the multiplicities of irreducible constituents in terms of certain cohomology groups, and we also provide an algorithm to compute multiplicities, in terms of the affine Hecke algebra.

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Ulrich Goertz, Thomas J. Haines. 2004-02-09. The Jordan-Hoelder series for nearby cycles on some Shimura varieties and affine flag varieties. https://arxiv.org/abs/math/0402143

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