共查询到20条相似文献,搜索用时 15 毫秒
1.
Let G be a reductive real Lie group, an involutive automorphism of G, and L=G
the fixed point set of . It is shown that G has only finitely many L-conjugacy classes of parabolic subgroups, so if P is a parabolic subgroup of G then there are only finitely many L-orbits on the real flag manifold G/P. This is done by showing that G has only finitely many L-conjugacy classes of -stable Cartan subgroups. These results extend known facts for the case where G is a complex group and L is a real form of G.Research partially supported by NSF Grant GP-16651. 相似文献
2.
TIM BRATTEN 《Compositio Mathematica》1997,106(3):283-319
Let G be a complex reductive linear algebraic group and
a real form. Suppose P is a parabolic subgroup of G and assume that P has a Levi factor L such that
is a real form of L.Using the minimal globalization V
min of a finite length admissible representation for L
0, one can define a homogeneous analytic vector bundle on the G
0 orbit S of P in the generalized flag manifold
. Let
denote the corresponding sheaf of polarized sections. In this article we analyze the G
0 representations obtained on the compactly supported sheaf cohomology groups
. 相似文献
3.
Goutam Mukherjee 《Proceedings Mathematical Sciences》1995,105(4):381-391
We consider certain natural (ℤ2)n actions on real Grassmann and flag manifolds andS
1 actions on complex Grassmann manifolds with finite stationary point sets and determine completely which of them bound equivariantly. 相似文献
4.
5.
Let G be a linear algebraic group over C and P be a parabolic subgroup. We determine the signatures of the flag manifold G/P. As an application, we prove that the nonsingular hypersurfaces of degree 2 in CP^n are prime if n satisfies certain conditions. 相似文献
6.
7.
For a complex semisimple Lie group and a real form we define a Poisson structure on the variety of Borel subgroups of with the property that all -orbits in as well as all Bruhat cells (for a suitable choice of a Borel subgroup of ) are Poisson submanifolds. In particular, we show that every non-empty intersection of a -orbit and a Bruhat cell is a regular Poisson manifold, and we compute the dimension of its symplectic leaves.
8.
On any manifold, any nondegenerate symmetric 2-form (metric) and any nondegenerate skew-symmetric differential form ω can
be reduced to a canonical form at any point but not in any neighborhood: the corresponding obstructions are the Riemannian
tensor and dω. The obstructions to flatness (to reducibility to a canonical form) are well known for any G-structure, not
only for Riemannian or almost symplectic structures. For a manifold with a nonholonomic structure (nonintegrable distribution),
the general notions of flatness and obstructions to it, although of huge interest (e.g., in supergravity) were not known until
recently, although particular cases have been known for more than a century (e.g., any contact structure is nonholonomically
“flat”: it can always be reduced locally to a canonical form). We give a general definition of the nonholonomic analogues
of the Riemann tensor and its conformally invariant analogue, the Weyl tensor, in terms of Lie algebra cohomology and quote
Premet’s theorems describing these cohomologies. Using Premet’s theorems and the SuperLie package, we calculate the tensors
for flag manifolds associated with each maximal parabolic subalgebra of each simple Lie algebra (and in several more cases)
and also compute the obstructions to flatness of the G(2)-structure and its nonholonomic superanalogue.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 153, No. 2, pp. 186–219, November, 2007. 相似文献
9.
Let M = G/K be a homogeneous differentiable manifold. We consider the homogeneous bundle = (G, π, G/K, K) and the tangent bundle τ
G/K of M = G/K, and give some results about the existence of homogeneous vectors on the fiber space of τ
G/K, for both cases of G semisimple and weakly semisimple.
相似文献
10.
11.
Thierry Levasseur 《Transactions of the American Mathematical Society》2001,353(10):4189-4202
Let be a semisimple complex Lie algebra with adjoint group and be the algebra of differential operators with polynomial coefficients on . If is a real form of , we give the decomposition of the semisimple -module of invariant distributions on supported on the nilpotent cone.
12.
13.
《Indagationes Mathematicae》2019,30(4):669-705
In this paper, we define locally convex vector spaces of weighted vector fields and use them as model spaces for Lie groups of weighted diffeomorphisms on Riemannian manifolds. We prove an easy condition on the weights that ensures that these groups contain the compactly supported diffeomorphisms. We finally show that for the special case where the manifold is the euclidean space, these Lie groups coincide with the ones constructed in the author’s earlier work (Walter, 2012). 相似文献
14.
15.
In this paper we classify the subsemigroups of any connected semisimple Lie groupG which areK-bi-invariant, whereG=KAN is an Iwasawa decomposition ofG. 相似文献
16.
Karl-Hermann Neeb 《Semigroup Forum》2008,77(1):5-35
A host algebra of a topological group G is a C
*-algebra whose representations are in one-to-one correspondence with certain continuous unitary representations of G. In this paper we present an approach to host algebras for infinite dimensional Lie groups which is based on complex involutive
semigroups. Any locally bounded absolute value α on such a semigroup S leads in a natural way to a C
*-algebra C
*(S,α), and we describe a setting which permits us to conclude that this C
*-algebra is a host algebra for a Lie group G. We further explain how to attach to any such host algebra an invariant weak-*-closed convex set in the dual of the Lie algebra
of G enjoying certain nice convex geometric properties. If G is the additive group of a locally convex space, we describe all host algebras arising this way. The general non-commutative
case is left for the future.
To K.H. Hofmann on the occasion of his 75th birthday 相似文献
17.
Yusuf Civan 《Proceedings of the American Mathematical Society》2006,134(5):1537-1548
We study the enumeration problem of stably complex structures on bounded flag manifolds arising from omniorientations, and determine those induced by almost complex structures. We also enumerate the stably complex structures on these manifolds which bound, therefore representing zero in the complex cobordism ring .
18.
Wo prove that there do not exist quasi-isometric embeddings of connected nonabelian nilpotent Lie groups equipped with left invariant Riemannian metrics into a metric measure space satisfying the curvature-dimension condition RCD(Q,N)with N∈R and N>1.In fact,we can prove that a sub-Riemannian manifold whose generic degree of nonholonomy is not smaller than 2 cannot be bi-Lipschitzly embedded in any Banach space with the Radon-Nikodym property.We also get that every regular sub-Riemannian manifold do not satisfy the curvature-dimension condition CD(K,N),where K,N∈R and N>1.Along the way to the proofs,we show that the minimal weak upper gradient and the horizontal gradient coincide on the Carnot-Caratheodory spaces which may have independent interests. 相似文献
19.
A. I. Shtern 《Mathematical Notes》2006,80(3-4):435-441
It is proved that an arbitrary pseudocharacter on a semisimple Lie group is continuous. 相似文献
20.
A family of transitive modular Lie superalgebras with depth one 总被引:1,自引:0,他引:1
Wen-de LIU~ 《中国科学A辑(英文版)》2007,50(10):1451-1466
The embedding theorem is established for Z-graded transitive modular Lie superalgebras g=(?)satisfying the conditions: (i)g0(?)(g-1)and g0-module g-1 is isomorphic to the natural(?)(g-1)-module; (ii)dim g1=2/3n(2n~2 1),where n=1/2dim g-1. In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian superalgebras.The restricted Lie superalgebras are also considered. 相似文献