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Results tagged with langlands-conjectures
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user 3545
Higher reciprocity laws
7
votes
Accepted
Langlands product
Basically, no. Marc Palm's answer addresses L-functions, but that is a long long way from determining the irrep -- you'd need L-functions and epsilon-factors of twists, plus an impressive ability to …
- 13.3k
6
votes
Characterizing the Local Langlands Correspondence
This answer will necessarily be full of conjecture, but I'll try to make things more concrete for some classical groups.
For a reductive group $G$, and smooth irreducible representation $(\pi, V)$ of …
- 13.3k
9
votes
Accepted
The simplest even Artin representations of degree 2 and the corresponding Maaß forms
I'll leave the dihedral and octahedral case to others, but for the tetrahedral ($A_4$) and icosahedral ($A_5$) case, I can give some answer.
For the tetrahedral case, the smallest conductor is 163. …
- 13.3k
7
votes
1
answer
959
views
Semisimple Weil-Deligne representations
I've just realized that I don't understand something important and basic about the Weil-Deligne group and its representations. (I'm not very surprised by this).
Following Deligne's article, Section …
- 13.3k
6
votes
Does local Langlands functoriality preserve genericity?
The general conjectural picture is the Gross-Prasad conjecture, found in Section 2 of Gross and Prasad's paper "On the decomposition of a representation of $SO_n$ when restricted to $SO_{n−1}$."
The …
- 13.3k
14
votes
Accepted
Local Langlands for $GL(2,\mathbf{C})$ and reducible principal series
This is a common point of confusion, and the OP is on exactly the right track.
A good reference for the representation theory is Chapter 1, Section 6, of Jacquet-Langlands book "Automorphic forms on …
- 13.3k
12
votes
What are the local Langlands conjectures nowadays, for connected reductive groups over a $p$...
First, I'd like to second the reference given by JT: David Vogan, "The local Langlands conjecture", appearing in Representation Theory of Groups and Algebras (J. Adams et al., eds. Contemporary Mathe …
- 13.3k
11
votes
Accepted
Langlands correspondence for higher local fields?
The Langlands correspondence for higher local fields is still at an early stage of development. I haven't really kept up with it, but here's some key points.
As the question stated, and Loren commen …
- 13.3k