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6
votes
0answers
212 views

Intersections of anisotropic tori with split Levi subgroups

Let G be a connected reductive group defined and split over a finite field k with Frobenius morphism F. Let T be an F-stable minisotropic maximal torus. Let P be an F-stable proper parabolic ...
7
votes
1answer
214 views

When is a Moy-Prasad filtration subgroup the stabilizer of a subset of the building (up to center)?

Let $G$ be a connected, simply connected, semi-simple algebraic group defined and split over a local non-arch field $k$ with integer ring $R$. Let $B$ be the corresponding reduced building. Fix an ...
4
votes
1answer
391 views

Representations of reductive groups over local fields through parahoric induction

Let me take $G$ to be a simple (connected) split reductive group over a local field $K$. One way I might go about constructing a (smooth, admissible) complex representation $\sigma$ of $G$ is as ...
0
votes
1answer
439 views

Closed subgroups of a $p$-adic algebraic group

Let $F$ be a finite extension of $\mathbb{Q}_p$ and $G$ the group of rational points of an algebraic group defined over $F$, endowed with the natural topology. Any Zariski closed subgroup $H \subset ...
2
votes
3answers
664 views

The Weyl group of $SL(2, F)$

Let $G= SL(2, F)$, given a torus $T$, the Weyl group with respect to $T$ is defined to be $W=N(T)/Z(T)$, the quotient of the normalizer $N(T)$ of the torus by the centralizer $Z(T)$ of the torus. My ...
3
votes
0answers
151 views

Reference request - Jacquet module and asymptotic of matrix coefficients

Hello, I would like to know some nice references about the relation between asymptotics of matrix coefficients of representations of reductive groups over local fields, and the pairing between the ...
4
votes
0answers
488 views

Newton Method in $p$-adic case

The Newton Method over $\mathbb{R}$ has the property that the precision is doubled (under some continuous differentialbe assumption) in each iteration. For the ring $\mathbb{Z}_p$ of $p$-adic ...
1
vote
1answer
533 views

Is Q_r algebraically isomorphic to Q_s while r and s denote different primes? [closed]

It is obvious that Q_r is topologically isomorphic to Q_s while r and s denote different primes.But I really don't know whether it is true in the aspect of algebra.As I failed to prove it,I think that ...
4
votes
4answers
634 views

cuspidal types and Iwahori subgroup for $SL(2,F)$

Let $(J,\pi)$ be a cuspidal type in $SL(2,F)$, $F$ is a non-Arch. local field and let $I$ be the Iwahori subgroup of $SL(2,F)$. Is there any possibility that $J\subset I$ or even a subgroup?
3
votes
1answer
631 views

Discrete Series representations for $SL_{2}$ over $p$-adic field.

I am working on the chamber homology for $SL(2,F)$, and stuck at some basic stuff on D.S. reps of $SL(2,F)$. Let $ I=\left( \begin{array}{cc} \mathcal{O}_{F} & \mathcal{O}_{F} \\ ...