Learn More
Let G denote a connected reductive group over a nonarchimedean local field F. Let K denote a special maximal parahoric subgroup of G(F). We establish a Satake isomorphism for the Hecke algebra HK of K-bi-invariant compactly supported functions on G(F). The key ingredient is a Cartan decomposition describing the double coset space K\G(F)/K. We also describe(More)
This thesis proves that the nearby cycles complex on a certain family of PEL local models is central with respect to the convolution product of sheaves on the corresponding affine flag variety. As a corollary, the semisimple trace function defined using the action of Frobenius on that nearby cycles complex is, via the sheaf-function dictionary, in the(More)
  • 1