Some results on the admissible representations of non-connected reductive p-adic groups

Details Some results on the admissible representations of non-connected reductive p-adic groups Some results on the admissible representations of non-connected reductive p-adic groups

1995-11-09

arxiv.org/abs/math/9511216v1

Mathematics

Representation Theory

Scientific paper

We examine the theory of induced representations for non-connected reductive $p$-adic groups for which $G/G^0$ is abelian. We first examine the structure of those representations of the form $\Ind_{P^0}^G(\sigma),$ where $P^0$ is a parabolic subgroup of $G^0$ and $\s$ is a discrete series representation of the Levi component of $P^0.$ Here we develop a theory of $R$--groups, extending the theory in the connected case. We then prove some general results in the theory of representations of non-connected $p$-adic groups whose component group is abelian. We define the notion of cuspidal parabolic for $G$ in order to give a context for this discussion. Intertwining operators for the non-connected case are examined and the notions of supercuspidal and discrete series are defined. Finally, we examine parabolic induction from a cuspidal parabolic subgroup of $G.$ Here we also develop a theory of $R$--groups, and show that these groups parameterize the induced representations in a manner that is consistent with the connected case and with the first set of results as well.

Affiliated with

Also associated with

No associations

Rating

Some results on the admissible representations of non-connected reductive p-adic groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Some results on the admissible representations of non-connected reductive p-adic groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Some results on the admissible representations of non-connected reductive p-adic groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-472846