Parahoric Restriction for GSp(4)

On Parahoric Subgroups

We give the proofs of some simple facts on parahoric subgroups and on Iwahori Weyl groups used in [H], [PR] and in [R]. 2000 Mathematics Subject Classification: Primary 11E95, 20G25; Secondary 22E20. Let G be a connected reductive group over a strictly henselian discretely valued field L. Kottwitz defines in [Ko] a functorial surjective homomorphism (1) κG : G(L) −→ X (Ẑ(G)). Here I = Gal(L̄/L) ...

Integral representation for L-functions for GSp4 ×GL2, II

Based on Furusawa’s theory [7], we present an integral representation for the L-function L(s, π× τ), where π is a cuspidal automorphic representation on GSp4 related to a holomorphic Siegel modular form, and where τ is an arbitrary cuspidal automorphic representation on GL2. As an application, a special value result for this L-function in the spirit of Deligne’s conjecture is proved.

Shimura Varieties with Parahoric Level

This survey article is intended to introduce the reader to several important concepts relating to Shimura varieties with parahoric level structure at p. The main tool is the Rapoport-Zink local model [RZ], which plays an important role in several aspects of the theory. We discuss local models attached to general linear and symplectic groups, and we illustrate their relation to Shimura varieties...

Reduction of Shimura varieties at parahoric levels

The Satake Isomorphism for Special Maximal Parahoric Hecke Algebras

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 how our results relate to the trea...