ISSN:
1436-5081
Keywords:
22E15
;
20M20
;
Symmetric space
;
flag manifold
;
compression semigroup
;
open orbits
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Let (G, H) be an irreducible semisimple symmetric pair,P $$ \subseteq$$ G a parabolic subgroup. Suppose that theL-orbit of the base point in the flag manifoldG/P is open and writeS(L,P)={g∈G:gL $$ \subseteq$$ LP} for the compression semigroup of this orbit. We show that ifP is minimal andS(L, P)=G, then (G, H) is Riemannian and we give a geometric characterization of those cases whereS(L, P) has non-empty interior different fromG. IfG/H is a symmetric space of regular type, then we show under certain additional assumptions thatS(L, Q) is an Ol'shanskiî semigroup.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01293670
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