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A note on Integral Satake isomorphisms

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arxiv 2005.13056 v3 pith:EN4TFBHX submitted 2020-05-26 math.RT

Xinwen Zhu This is my paper · ORCID
classification math.RT
keywords algebraheckeintegralsatakeadicalgebraicdescriptionformulate
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abstract

We formulate a Satake isomorphism for the integral spherical Hecke algebra of an unramified $p$-adic group $G$ and generalize the formulation to give a description of the Hecke algebra $H_G(V)$ of weight $V$, where $V$ is a lattice in an irreducible algebraic representation of $G$.

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  1. Crystalline lifts of semisimple $G$-valued Galois representations with fixed determinant

    math.NT 2024-12 conditional novelty 6.0 of 10

    A proof that quasi-semisimple mod p G-valued Galois representations admit crystalline lifts with arbitrary fixed crystalline abelianization, for split reductive groups and tame quasi-split groups.

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