1
vote
0answers
109 views

Clarification about Tits' article in the Corvallis

I am studying Tits' article in the Corvallis wherein he defines the apartment in the general case (not necessarily split). I wish to know what he means about the filtration of the groups $U_a(K)$ ...
1
vote
0answers
127 views

Algebraic characters and quasi-characters of reductive algebraic group over non-archimedean local field

Let $G$ be a reductive algebraic group over $F$, where $F$ is a non-archimedean local field. Then $G(F)$ is a p-adic group. Let $\Psi(G)$ be the lattice of algebraic characters. Let $\Lambda_G$ be the ...
4
votes
4answers
622 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
619 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} \\ ...