Minimal representations via Bessel operators

Details Minimal representations via Bessel operators Minimal representations via Bessel operators

2011-06-18

arxiv.org/abs/1106.3621v3

Mathematics

Representation Theory

Scientific paper

We construct an L^2-model of "very small" irreducible unitary representations of simple Lie groups G which, up to finite covering, occur as conformal groups Co(V) of simple Jordan algebras V. If $V$ is split and G is not of type A_n, then the representations are minimal in the sense that the annihilators are the Joseph ideals. Our construction allows the case where G does not admit minimal representations. In particular, applying to Jordan algebras of split rank one we obtain the entire complementary series representations of SO(n,1)_0. A distinguished feature of these representations in all cases is that they attain the minimum of the Gelfand--Kirillov dimensions among irreducible unitary representations. Our construction provides a unified way to realize the irreducible unitary representations of the Lie groups in question as Schroedinger models in L^2-spaces on Lagrangian submanifolds of the minimal real nilpotent coadjoint orbits. In this realization the Lie algebra representations are given explicitly by differential operators of order at most two, and the key new ingredient is a systematic use of specific second-order differential operators (Bessel operators) which are naturally defined in terms of the Jordan structure.

Affiliated with

Also associated with

No associations

Rating

Minimal representations via Bessel operators 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 Minimal representations via Bessel operators, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Minimal representations via Bessel operators will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-465425