Theta Correspondence and Quantum Induction

Details Theta Correspondence and Quantum Induction Theta Correspondence and Quantum Induction

2002-10-23

arxiv.org/abs/math/0210370v3

Advances in Math. 2005

Mathematics

Representation Theory

31 pages

Scientific paper

In his article "Transcending Classical Invariant Theory" (J.A.M.S., 1989, Vol 2), Roger Howe established a correspondence between representations of a dual pair of reductive groups. This correspondence is known as Howe's correspondence or local theta correspondence. In my paper "Unitary Representations and Theta Correspondence for Classical Group of Type I"(to appear in J. Func. Anal.), we proved that theta correspondence over the real field preserves unitarity under certain restrictions, generalizing some results of Jian-Shu Li (Invent. Math., Vol 97, 1989). In this paper, we study the compositions of theta correspondences. Under certain favorable conditions, we prove that the composition of theta correspodence yields unitary representations. We call this process quantum induction. Quantum induction resembles parabolic induction in various ways. Some results in this paper were announced at ICM-2002.

Affiliated with

Also associated with

No associations

Rating

Theta Correspondence and Quantum Induction 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 Theta Correspondence and Quantum Induction, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Theta Correspondence and Quantum Induction will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-640136