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2 votes
0 answers
73 views

Number of rational points of a connected reductive group in a compact subset

Let $G$ be a connected reductive $\mathbb{Q}$-group. Let $\mathbb{A}$ denote the ring of adèles of $\mathbb{Q}$. Let $B \subset G(\mathbb{A})$ be a compact, let $x \in G(\mathbb{A})$ and consider the ...
Sentem's user avatar
  • 81
4 votes
1 answer
299 views

Can any pair of associate parabolics be related by opposite parabolics?

Let $G$ be a reductive group, say over an algebraically closed field of characteristic zero. We have the following definitions for a pair of parabolic subgroups $P_1$ and $P_2$ with Levi quotients $...
Anthony Blanche's user avatar
5 votes
2 answers
737 views

What condition makes unitary reductive group unramified?

I am a little bit confused with the definition of an unramified unitary group. Let $F$ be a local field of characteristic zero whose residue field is finite field of characteristic $p$. Then for a ...
Monty's user avatar
  • 1,759
2 votes
0 answers
418 views

How can this argument calculating the Haar measure on a parabolic subgroup be generalized to the non-split case?

Let $\mathbf G$ be a connected, reductive group over a local field $F$. Assume there is a maximal torus $\mathbf T$ which is split over $F$. Let $\mathbf P$ be a parabolic subgroup of $\mathbf G$ ...
D_S's user avatar
  • 6,180
17 votes
2 answers
3k views

What's the point of a Whittaker model?

Let $G$ be a quasi-split connected reductive group over a $p$-adic field $F$. Let $B$ be a Borel subgroup which is defined over $F$, with $B = TU$, $T$ defined over $F$. The choice of $T$ and $B$ ...
D_S's user avatar
  • 6,180
3 votes
1 answer
611 views

How to translate the representation theory of semisimple to reductive groups?

I am aware of the following question: Definitions of Reductive and Semisimple Groups So let me phrase a precise question: Is there a standard technique by which one can translate the unitary/...
Marc Palm's user avatar
  • 11.2k