Mathematics – Representation Theory
Scientific paper
2008-09-08
Mathematics
Representation Theory
13 pp, Ref.18
Scientific paper
We describe a general construction of irreducible unitary representations of the group of currents with values in the semidirect product of a locally compact subgroup $P_0$ and a one-parameter group ${\mathbb R {}}^*_+=\{r:r>0\}$ of automorphisms of $P_0$. This construction is determined by a a faithful unitary representation of $P_0$ (canonical representation) whose images under the action of the group of automorphisms tend to the identity representation as $r\to 0$. We apply this construction to the groups of currents of the maximal parabolic subgroups of the groups of motions of the $n$-dimensional real and complex Lobachevsky spaces. The obtained representations of the groups of parabolic currents can be uniquely extended to the groups of currents with values in the semisimple groups O(n,1) and U(n,1). This gives a new description of the representations of the groups of currents of these groups constructed in the 70s and realized in the Fock space. The key role in our construction is played by the so-called special representation of the parabolic subgroup $P$ and the remarkable $\sigma$-finite measure (Lebesgue measure) $\mathcal L$ in the space of distributions.
Graev Mark I.
Vershik Anatoly M.
No associations
LandOfFree
Integral models of unitary representations of current groups with values in semidirect products 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 Integral models of unitary representations of current groups with values in semidirect products, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Integral models of unitary representations of current groups with values in semidirect products will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-31068