The Geometric Satake Correspondence for Ramified Groups

By Xinwen Zhu. 2011

62 citations recorded by the source corpus.

We prove the geometrical Satake isomorphism for a reductive group defined over F=k((t)), and split over a tamely ramified extension. As an application, we give a description of the nearby cycles on certain Shimura varieties via the Rapoport-Zink-Pappas local models.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/70ebd6bb838a92639dfb901906203b20c1a01255

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Timo Richarz
2. Thomas J. Haines
3. Xuhua He

In Mathematical Physics

1. Timo Richarz
2. Thomas J. Haines
3. Xuhua He
4. Michael Rapoport
5. Georgios Pappas
6. Xinwen Zhu
7. E. Viehmann

Citations in the corpus

• The test function conjecture for parahoric local models (2018, methodology): “For general quasisplit groups G, but now very special level G, our main theorem below reduces to [PZ13, 10.4.5], [Zhu15, §6].”
• Cycles on Shimura varieties via geometric Satake (2017, unknown): “Using the fact that the natural map T̂ σ/T̂ σ,◦ → Ĝσ/Ĝσ,◦ is an isomorphism (see [Zhu15, Lemma 4.6]), the usual highest weight theory for representations of a connected reductive group extends to Ĝσ without change (see [Zhu15, Lemma 4.10]).”