On the realisation of maximal simple types and epsilon factors of pairs

Details On the realisation of maximal simple types and epsilon factors of pairs On the realisation of maximal simple types and epsilon factors of pairs

2006-03-02

arxiv.org/abs/math/0603051v1

Mathematics

Representation Theory

55 pages

Scientific paper

Let $G$ be the group of rational points of a general linear group over a non-archimedean local field $F$. We show that certain representations of open, compact-mod-centre subgroups of $G$, (the maximal simple types of Bushnell and Kutzko) can be realized as concrete spaces. In the level zero case our result is essentially due to Gelfand. This allows us, for a supercuspidal representation $\pi$ of $G$, to compute a distinguished matrix coefficient of $\pi$. By integrating, we obtain an explicit Whittaker function for $\pi$. We use this to compute the epsilon factor of pairs, for supercuspidal representations $\pi_1$, $\pi_2$ of $G$, when $\pi_1$ and the contragredient of $\pi_2$ differ only at the `tame level' (more precisely, $\pi_1$ and $\check{\pi}_2$ contain the same simple character). We do this by computing both sides of the functional equation defining the epsilon factor, using the definition of Jacquet, Piatetskii-Shapiro, Shalika. We also investigate the behaviour of the epsilon factor under twisting of $\pi_1$ by tamely ramified quasi-characters. Our results generalise the special case $\pi_1=\check{\pi}_2$ totally wildly ramified, due to Bushnell and Henniart.

Affiliated with

Also associated with

No associations

Rating

On the realisation of maximal simple types and epsilon factors of pairs 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 On the realisation of maximal simple types and epsilon factors of pairs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On the realisation of maximal simple types and epsilon factors of pairs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-369429