S. Helgason. Differential geometry, Lie groups, and symmetric spaces. Academic Press, 1978. Home/Search Document Not in Database Summary Related Articles Check |
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Berger algebras, weak-Berger algebras and Lorentzian holonomy - Leistner (2002) (Correct)
....gives the following proposition, which will be veri ed in the appendix. Proposition 3.3. The compact real forms of the algebras in table 2 and the reelli cation of the representations are equivalent to the holonomy representations of the following Riemannian, hermitian symmetric spaces (see [Hel78]) Type non compact compact dim. 1. BD I SO 0 (2; n) SO(2) SO(n) SO(2 n) SO(2) SO(n) 2n 2. C I Sp(n; U(n) Sp(n) U(n) n(n 1) 3. D III SO (2n) U(n) SO(2n) U(n) n(n 1) 4. A III SU(n; m) U(n) U(m) SU(n m) U(n) U(m) 2nm 5. E III e 6. E V II e 7( 25) ....
.... one gets that Id = Id and E ij = E ij : Q ( e i ) e i ) Id = Id = Q ( e i ) e i ) Q ( e i ) e j ) E ij = E ij = E ji = Q ( e j ) e i ) Riemannian symmetric space of type BD I given by the quotient SO(2 n) SO(2) SO(n) For this and the following symmetric spaces see [Hel78]. Its tangent space is equal to so(n 2; 4 0 0 a X a 0 Y X Y B A 3 5 7 (X; Y ) 29 with X;Y 2 , a 2 and B 2 so(n; R) Therefore the holonomy representation of , given by the adjoint representation is R) R 2n 0 1 1 0 (X; Y ) Y; X) ....
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S. Helgason. Di erential Geometry, Lie Groups, and Symmetric Spaces. Academic Press, 1978.
Unknown - (Correct)
....pk 1 , and hence g # g = p P , since the centralizer G g # G : #(g) g coincides with K [12, p.305] So g # : #(g 1 ) #(g) 1 , g # ) # = g, fg) # = g # f # , g # ) g ) # , for all f, g G, n positive integer. Since # is the di#erential of # at the identity, we have [7, 110] for all A g. So ) # = #(e A ) e #A . We now claim for any g G, and any natural number n, 3.2) g . The relation g is known in [13, p.448] and we use similar idea (indeed the original idea can be found in [17] when G = SL(n, C) to establish (3.2) We denote by # # ....
S. Helgason, Di#erential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978.
Newton's Method on Riemannian Manifolds: - Covariant Alpha-Theory Jean-Pierre (Correct)
....we have to de ne the corresponding invariants in the context of Riemannian manifolds. The material contained in this section is classical in Riemannian geometry. The reader is refered to a textbook on this subject, for example: Dieudonn e [7] Do Carmo [8] Gallot Hulin Lafontaine [11] Helgason [12], O Neill [21] De nition 1.1 (Tensors. The space of p contravariant and q covariant analytic tensor elds T : T (M n ) T (M n ) F(M n ) is denoted by T q (M n ) An m tuple of such tensor elds is called a vectorial tensor eld and the space of vectorial tensor elds is denoted ....
Helgason, K., Di erential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, 1979.
Differential Recursion Relations For Laguerre Functions On.. - Davidson, Olafsson (2002) (Correct)
....This system generalizes the classical Laguerre operator, however, the raising and lowering operators are not discussed. 1. SU(n; n) and its Lie Algebra We keep the notation from the introduction but specialize to the case G = SU(n; n) The standard de nition of SU(n; n) as found on page 444 of [5] acts naturally on the generalized unit disk. Our de nition below is suited for the right half plane action and is conjugate to the standard version by the Cayley transform. The group SU(n; n) is thus de ned as follows: Let J = SU(n; n) fg 2 SL(2n; j gJg = Jg : We frequently write g 2 ....
S. Helgason,Di erential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, 1978.
The Heat Kernel on Noncompact Symmetric Spaces - Anker, Ostellari (Correct)
....for their great job, as well as Martine Babillot, Gilles Carron, Sasha Grigor yan and Jean Pierre Otal for stimulating discussions. 1. Preliminaries We shall briefly review some basics about noncompact Riemannian symmetric spaces X = G K and we shall otherwise refer to standard texbooks ( GV] [H1], H2] H3] Kn] for their structure and harmonic analysis thereon. Thus G is a semisimple Lie group (real, connected, noncompact, with finite center) or more generally a reductive Lie group in the Harish Chandra class and K is a maximal compact subgroup. Let # be the Cartan involution and let ....
S. Helgason, Di#erential geometry, Lie groups, and symmetric spaces, Academic Press (1978).
Anti Holomorphic Multiplication And A Real Algebraic Modular.. - Goresky, Tai (Correct)
....[RoS] GT1] 3.5. Theorem. Suppose # is torsion free. Then the association f # determines a one to one correspondence between the cohomology set H (###, #) and the connected components of the fixed point set X . 3.6. Proof. The twisted involution ## : E E acts by isometries so ([H] I 13.5) the fixed point set E is nonempty. If x, x # then the unique geodesic joining them is also fixed by ##,soE is connected. Its image in X is a connected subset X(##)ofX which depends only on the cohomology class of f # . It is easy to check that f # and f # # are ....
S. Helgason, Di#erential Geometry, Lie Groups, and Symmetric Spaces Academic Press, 1978.
The Action of Intertwining Operators on Spherical - Vectors In The (Correct)
.... f be minus the identity matrix in SL(2; C) Then using (14) one readily sees that j ff (f) Ad(f ff ) From f = I it now follows that Ad(f ff ) I: Let F = fk 2 Ad(K)jk = Ig: Then it is known that F = Ad(K) exp(iada 0 ) hence F is a finite abelian group that centralizes m 0 (cf. [9], p.435, Exercise A3) Since Ad maps the generators of F 0 into F; it follows that Ad(F 0 ) ae F; and all assertions follow. 9 For every ff 2 T P we define the smooth curve c ff : Gamma ] G=P by c ff (s) w ff exp[s(X ff X ff ) P: 16) Then c ff ( Gamma 2 ) eP and c ff ( 2 ) ....
S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces. Academic Press, New York, 1978.
Unspecified Journal - Volume Number Pages Self-citation (Lie) (Correct)
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S. Helgason, Di#erential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978.
Submitted to AUTOMATICA, July 20th, 1999 - The Geometry Of (Correct)
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S. Helgason. Differential geometry, Lie groups, and symmetric spaces. Academic Press, 1978.
An Ergodic Arnold{Liouville - Theorem For Locally (Correct)
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Helgason, S.: Di erential Geometry, Lie Groups, and Symmetric Spaces. Acad. Press, Orlando, 1978
A Riemannian Framework for Tensor Computing - Pennec, Fillard, Ayache (Correct)
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Helgason, S. (1978). Dierential Geometry, Lie groups, and Symmetric Spaces. Academic Press.
The structure of Lie algebras and the classification.. - Basarab-Horwath.. (2000) (Correct)
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Helgason S. Di#erential Geometry, Lie Groups, and Symmetric Spaces. Academic Press, New York, 1978.
Towards a Classification of Lorentzian holonomy groups - Leistner (2003) (1 citation) (Correct)
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Sigurdur Helgason. Di erential Geometry, Lie Groups, and Symmetric Spaces. Academic Press, 1978.
Chern Classes of Automorphic Vector Bundles - Goresky, Pardon (2002) (Correct)
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S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, 1978
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Helgason S., Di#erential geometry, Lie groups, and symmetric spaces, Academic Press, New York (1978).
Towards a Classification of Lorentzian holonomy groups. Part II: .. - Leistner (2003) (1 citation) (Correct)
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Sigurdur Helgason. Di erential Geometry, Lie Groups, and Symmetric Spaces. Academic Press, 1978.
LOWER BOUNDS FOR THE CURVATURE INVARIANT p(G/K) - Associated With Riemannian (Correct)
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S. Helgason, Di#erential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York (1978).
Unknown - (Correct)
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S. Helgason, Di#erential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978.
A Variational Approach for Compact Homogeneous Einstein.. - Böhm, Wang, Ziller (Correct)
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S. Helgason, Di#erential geometry, Lie groups, and symmetric spaces, Academic Press New-York and London, second edition, (1978).
Page 1] Laws of Trigonometry in Symmetric - Spaces Helmer Aslaksen (Correct)
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Helgason, S., Di#erential Geometry, Lie Groups, and Symmetric Spaces. Academic Press, New York, 1978.
Unspecified Journal Volume 00, Number 0, Pages 000--000 .. - Ez-Horn-Mirsky's.. (Correct)
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S. Helgason, Di#erential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978.
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Sigurdur Helgason, Differential geometry, Lie groups, and symmetric spaces (Academic Press, New York, 1978).
Analysis on Tube Domains over Light Cones: Some Extensions of .. - Bekolle, Bonami (Correct)
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S. Helgason, Di erential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York (1978).
Harmonic analysis on semisimple symmetric spaces - .. - van den Ban.. (Correct)
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S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, San Francisco, London, 1978.
Rational Orbit Decompositions Of Prehomogeneous Vector Spaces - Yukie (Correct)
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Helgason, S. Differential geometry, Lie groups, and symmetric spaces. Academic Press, New York, San Francisco, London, 1978.
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