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Finite orbit decomposition of real flag manifolds

Bernhard Krötz, Henrik Schlichtkrull (2016)

Journal of the European Mathematical Society

Let G be a connected real semi-simple Lie group and H a closed connected subgroup. Let P be a minimal parabolic subgroup of G . It is shown that H has an open orbit on the flag manifold G / P if and only if it has finitely many orbits on G / P . This confirms a conjecture by T. Matsuki.

Flexibility of surface groups in classical simple Lie groups

Inkang Kim, Pierre Pansu (2015)

Journal of the European Mathematical Society

We show that a surface group of high genus contained in a classical simple Lie group can be deformed to become Zariski dense, unless the Lie group is S U ( p , q ) (resp. S O * ( 2 n ) , n odd) and the surface group is maximal in some S ( U ( p , p ) × U ( q - p ) ) S U ( p , q ) (resp. S O * ( 2 n - 2 ) × S O ( 2 ) S O * ( 2 n ) ). This is a converse, for classical groups, to a rigidity result of S. Bradlow, O. García-Prada and P. Gothen.

Function spaces on the Olśhanskiĭsemigroup and the Gel'fand-Gindikin program

Khalid Koufany, Bent Ørsted (1996)

Annales de l'institut Fourier

For the scalar holomorphic discrete series representations of SU ( 2 , 2 ) and their analytic continuations, we study the spectrum of a non-compact real form of the maximal compact subgroup inside SU ( 2 , 2 ) . We construct a Cayley transform between the Ol’shanskiĭ semigroup having U ( 1 , 1 ) as Šilov boundary and an open dense subdomain of the Hermitian symmetric space for SU ( 2 , 2 ) . This allows calculating the composition series in terms of harmonic analysis on U ( 1 , 1 ) . In particular we show that the Ol’shanskiĭ Hardy space for U ( 1 , 1 ) is different...

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