Reciprocity laws for representations of finite groups

Details Reciprocity laws for representations of finite groups Reciprocity laws for representations of finite groups

2009-11-19

arxiv.org/abs/0911.3830v3

Annales des sciences mathematiques du Quebec 34 (2010), no 1, 37-61

Mathematics

Representation Theory

To appear in "Annales des sciences mathematiques du Quebec"

Scientific paper

Much has been written on reciprocity laws in number theory and their connections with group representations. In this paper we explore more on these connections. We prove a "reciprocity Law" for certain specific representations of semidirect products of two cyclic groups which is in complete analogy with classical reciprocity laws in number theory. In fact, we show that the celebrated quadratic reciprocity law is a direct consequence of our main theorem applied to a specific group. As another consequence of our main theorem we also recover a classical theorem of Sylvester. Our main focus is on explicit constructions of representations over sufficiently small fields. These investigations give further evidence that there is still much unexplored territory in connections between number theory and group representations, even at an elementary level.

Affiliated with

Also associated with

No associations

Rating

Reciprocity laws for representations of finite 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 Reciprocity laws for representations of finite groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Reciprocity laws for representations of finite groups will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-453656