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Results tagged with reductive-groups
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user 1384
A reductive group is an algebraic group $G$ over an algebraically closed field such that the unipotent radical of $G$ is trivial
18
votes
6
answers
2k
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Explicit formula for the trace of an unramified principal series representation of $GL(n,K)$...
Let $K$ be a non-arch local field (I'm only interested in the char 0 case), let $\mathbb{G}$ be a connected reductive group over $K$ and let $G=\mathbb{G}(K)$. If $V$ is a smooth irreducible complex r …
- 41.4k
10
votes
Accepted
Type of place versus type of unitary group
Things are perhaps a bit messier than you hope. In particular it is not true that the unitary group is non-quasi-split if and only if $v$ ramifies. Disclaimer: I did not know the answer to this questi …
- 41.4k
30
votes
Accepted
What's the point of a Whittaker model?
This question is a bit like saying "what's the point of the theory of bases for vector spaces -- this just gives you an isomorphism of your space with $\mathbb{R}^n$. What is the point of defining thi …
- 41.4k