Questions tagged [p-adic-local-langlands]
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6 questions
2 votes
0 answers
131 views
Reference request: compact representations of p-adic groups
I'm looking for a proof of the following claim: Let $G$ be a $p$-adic group and $W$ a smooth representation with compactly supported matrix coefficients (Bernstein calls these 'compact'). I want to ...
3 votes
1 answer
363 views
Bernstein classification and harmonic analysis
Let $G$ be a reductive group over a $p$ adic field $F$ ($GL_2$ is good enough for me). Then there is the Bernstein classification of irreducible representations by cuspidal data and also the ...
- 103
3 votes
0 answers
180 views
Hecke compatibility for p-adic local langlands
Both in the global geometric Langlands as well as the local ($l \neq p$) Langlands formulated in the paper Geometrization of the local Langlands correspondence by Fargues and Scholze, there is a ...
- 131
9 votes
0 answers
211 views
Can two irreps of a p-adic group with distinct cuspidal support have a non-trivial extension between them?
Let $G$ be a connected reductive algebraic group over a $p$-adic field $F$. All representations mentioned here are assumed to be smooth. Recall that a cuspidal pair $(M, \sigma)$ is a Levi subgroup $...
10 votes
0 answers
268 views
Differences between Banach and analytic $p$-adic local Langlands correspondence
I have been trying to understand the categorical $p$-adic local Langlands paper [EGH 23] and I have a question regarding the differences between the Banach and analytic case of the conjectured ...
- 131
3 votes
0 answers
190 views
Casimir eigenvalues of p-adic automorphic representations
In the context of p-adic local Langlands correspondence: Is it possible to define Casimir eigenvalues for p-adic automorphic representations? If a local representation arises from a global Galois ...
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