1,720,998 research outputs found
A remark on the orbit structure of the complexification of a semisimple symmetric space
No full textWe consider the action of a real semisimple Lie group G on the complexification G(C)/H-C of a semisimple symmetric space G/H and we present a refinement of Matsuki's results (Matsuki, 1997 [1]) in this case. We exhibit a finite set of points in G(C)/H-C, sitting on closed G-orbits of locally minimal dimension, whose slice representation determines the G-orbit structure of G(C)/H-C. Every such point (p) over bar lies on a compact torus and occurs at specific values of the restricted roots of the symmetric pair (g. h). The slice representation at (p) over bar is equivalent to the isotropy representation of a real reductive symmetric space, namely Z(G)(p(4))/G((p) over bar). In principle, this gives the possibility to explicitly parametrize all G-orbits in G(C)/H-C. (C) 2012 Elsevier B.V. All rights reserved
Invariant domains in the complexification of a noncompact Riemannian symmetric space
No full textLet G/K be a noncompact Riemannian symmetric space and let G(C)/K-C be its complexification. Then G acts on G(C)/K-C by left translations. We study the invariant CR-structure of the closed G-orbits of maximal dimension and determine which ones can lie in the boundary of an invariant Stein domain. In this way, we obtain information on the G-invariant Stein domains in G(C)/K-C. (C) 2002 Elsevier Science (USA)
A REMARK ON THE N-INVARIANT GEOMETRY OF BOUNDED HOMOGENEOUS DOMAINS
No full textLet D be a bounded homogeneous domain in Cn. In this note, we give a characterization of the Stein domains in D which are invariant under a maximal unipotent subgroup N of Aut(D). We also exhibit an Ninvariant potential of the Bergman metric of D, expressed in a Lie theoretical fashion. These results extend the ones previously obtained by the authors in the symmetric case
Invariant plurisubharmonic functions on non-compact Hermitian symmetric spaces
No full textLet G/K be an irreducible non-compact Hermitian symmetric space and let D be a K- invariant domain in G / K . In this paper we characterize several classes of K -invariant plurisubharmonic functions on D in terms of their restrictions to a slice intersecting all K -orbits. As applications we show that K -invariant plurisubharmonic functions on D are necessarily continuous and we reproduce the classification of Stein K -invariant domains in G/K obtained by Bedford and Dadok. (J Geom Anal 1:1–17, 1991)
Complex extensions of semisimple symmetric spaces
No full textLet G/H be a pseudo-Riemannian semisimple symmetric space. The tangent bundle T (G/H) contains a maximal G-invariant neighbourhood Omega of the zero section where the adapted-complex structure exists. Such Omega is endowed with a canonical G-invariant pseudo-Kahler metric of the same signature as the metric on G/H. We use the polar map phi : Omega -> G(C)/H-C to define a G-invariant pseudo-Kahler metric on distinguished G-invariant domains in G(C)/H-C or on coverings of principal orbit strata in G(C)/H-C. In the rank-one case, we show that the polar map is globally injective and the domain phi(Omega) subset of G(C)/H-C is an increasing union of q-complete domains
BLACK: A fast, flexible and reliable LTL satisfiability checker
Full text linkBLACK, short for Bounded Ltl sAtisfiability ChecKer, is a recently developed software tool for satisfiability checking of Linear Temporal Logic (LTL) formulas. It supports formulas using both future and past operators, interpreted over both infinite and finite traces. At its core, BLACK uses an incremental SAT encoding of the one-pass tree-shaped tableau for LTL recently developed by Reynolds, which guarantees completeness thanks to its particular pruning rule. This paper gives an overview of the tool, surveys the main design choices underlying its implementation, describes its features and discusses potential future developments
First-Order Automata
No full textFirst-order linear temporal logic (FOLTL) is a flexible and expressive formalism capable of naturally describing complex behaviors and properties. Although the logic is in general highly undecidable, the idea of using it as a specification language for the verification of complex infinite-state systems is appealing. However, a missing piece, which has proved to be an invaluable tool in dealing with other temporal logics, is an automaton model capable of capturing the logic. In this paper we address this issue, by defining and studying such a model, which we call first-order automaton. We define this very general class of automata, and the corresponding notion of regular first-order language (of finite words), showing their closure under most language-theoretic operations. We show how they can capture any FOLTL formula over finite words, over any signature and theory, and provide sufficient conditions for the semi-decidability of their non-emptiness problem. Then, to show the usefulness of the formalism, we prove the decidability of monodic FOLTL, a classic result known in the literature, with a simpler and direct proof
Some Transitive Linear Actions of Real Simple Lie Groups
No full textIn Moskowitz M., and R.Sacksteder, An extension of the Minkowski-Hlawka theorem, Mathematika 56 (2010), 203-216, essential use was made of the fact that in its natural linear action the real symplectic group, Sp(n,R), acts transitively on R-2n \ {0} (similarly for the theorem of Hlawka itself, SL(n, R) acts transitively on \ {01). This raises the natural question as to whether there are proper connected Lie subgroups of either of these groups which also act transitively on R-2n \ {0}, (resp. R-n \ {01}. Here we determine all the minimal ones. These are Sp(n, R) subset of SL(2n, R) and SL(n, C) subset of SL(2n, R) acting on R-2n \ {0}; on R-4n \ {0}, they are Sp(2n, R) subset of SL(4n, R) and SL(n, H)(= SU* (2n)) subset of SL(4n, R)
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