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3 questions
5
votes
1
answer
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Explicit Jacquet-Langlands correspondence for real reductive groups
Let $G$ be a connected reductive group over $\mathbb R$. Let $G'$ over $\mathbb R$ be an inner form of $G$ with ${}^LG={}^LG'$. By local Langlands correspondence over $\mathbb R$, if a $L$-packet of $...
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11
votes
0
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283
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Why are there so few irreducible admissible representations of $\text{GL}(n,\mathbb{R})$ (up to infinitesimal equivalence)?
Studying Langlands's classification of irreducible admissible representations, I have been rather stunned by the following:
Theorem
Up to infinitesimal equivalence, all irreducible admissible ...
- 511
6
votes
1
answer
764
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What is a map for the representation theory of reductive groups?
I have finished learning about linear algebraic groups (minus their representation theory) and the associated algebraic structures (root data, root systems, etc.), and will next attempt to summarize ...
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