Corrigendum: The base change fundamental lemma for central elements in parahoric Hecke algebras

A tale of parahoric--Hecke algebras, Bernstein and Satake homomorphisms

Let $\mathbf{G}$ be a connected reductive group over a {non-archimedean local field} $F$. Let $K_\mathcal{F}$ be the parahoric subgroup attached to a facet $\mathcal{F}$ in the Bruhat--Tits building of $\mathbf{G}$. The ultimate goal of the present paper is to describe the center of the parahoric--Hecke algebra $\mathcal{H}(\mathbf{G}(F)//K_{\mathcal{F}}, \mathbb{Z}[q^{-1}])$ with level $K_{\mathcal{F}}$ and prove the compatibility of generalized (twisted) Bernstein and Satake homomorphisms.

The base change fundamental lemma for central elements in parahoric Hecke algebras

Clozel and Labesse proved the base change fundamental lemma for spherical Hecke algebras attached to an unramified group over a p-adic field. This paper proves an analogous fundamental lemma for centers of parahoric Hecke algebras attached to the same class of groups. This provides an ingredient needed for the author's program to study Shimura varieties with parahoric level structure at p.

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 H 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 treatment of Cartier, where K is replaced by a special maximal compact open subgroup K' of G(F) and where a Satake isomorphism is established for the Hecke algebra of K'-bi-invariant compactly supported functions…

Nearby cycles of parahoric shtukas, and a fundamental lemma for base change

Using the Langlands-Kottwitz paradigm, we compute the trace of Frobenius composed with Hecke operators on the cohomology of nearby cycles, at places of parahoric reduction, of perverse sheaves on certain moduli stacks of shtukas. Following an argument of Ngo, we then use this to give a geometric proof of a base change fundamental lemma for parahoric Hecke algebras for GL_n over local function fields. This generalizes a theorem of Ngo, who proved the base change fundamental lemma for spherical Hecke algebras for GL_n over local function fields, and extends to positive characteristic (for GL_n) …

局部域上 Kac-Moody 群的完备 Iwahori-Hecke 代数与 parahoric Hecke 代数

Completed Iwahori-Hecke algebras and parahoric Hecke algebras for Kac-Moody groups over local fields

本文定义了局部域上 split Kac-Moody 群的 Iwahori-Hecke 代数完备化，利用 masure 工具确定其中心并证明同构于球面 Hecke 代数，同时将 Hecke 代数构造推广至特殊球面面。

中心动机在paraoric旗变种上

Central motives on parahoric flag varieties

本文提出了一种新的动机中心functor，通过Wakimoto动机证明其t-精确性，并提供了通用paraorics Hecke代数的新方法。