... those **symmetric** **spaces**, called here « special» , for which the method applies in the same way as for Lie ...general **spaces**, one needs to introduce a real- valued function e(X; Y ) of two tangent ...

204

... SPIN **SYMMETRIC** **SPACES** JEAN-LOUIS MILHORAT ...spin **symmetric** **spaces**, providing, for sym- metric **spaces** of “inner” type, a formula giving this first eigenvalue in terms of the algebraic ...

42

... HERMITIAN **SYMMETRIC** **SPACES** BRUNO DUCHESNE, JEAN LÉCUREUX, AND MARIA BEATRICE POZZETTI A BSTRACT ...Hermitian **symmetric** **spaces**, which allows us to define maximal ...Hermitian **symmetric** ...

50

... 1. Introduction It is well-known that **symmetric** **spaces** provide examples where detailed infor- mation on the spectrum of Laplace or Dirac operators can be obtained. Indeed, for those manifolds, the ...

9

... **spaces** are positively squared distance curved Philippe Delano¨ e † and Fran¸cois Rouvi` ere Abstract The squared distance curvature is a kind of two-point curvature the sign of which turned out crucial for the ...

14

... a **symmetric** strictly pseudoconvex CR manifold then M = G/K where G is the closed subgroup of P sH(M, θ) generated by all the pseudo-Hermitian symmetries ψ(x0), x0 ∈ M, and K is the isotropy subgroup at a base ...

42

... 6 Conclusion Across the paper, we have seen how wrapped models can be constructed on manifolds with an exponential map. We have analysed the case of the Lie group SE(n) and mentioned Riemannian manifolds, though such ...

13

... connection **spaces** to establish in Section 1 the approximation provided by one step of the pole ladder up to order ...locally **symmetric** space, this suggests that the error could vanish in this ...global ...

19

... SPIN **SYMMETRIC** **SPACES** JEAN-LOUIS MILHORAT ...irreducible **symmetric** space, endowed with the metric induced by the Killing form of G ...irreducible **symmetric** **spaces** endowed with a ...

18

... result of a least squares minimization and a recursive algorithm. In particular, we will focus on a special class of Riemannian **symmetric** **spaces**: the special orthogonal group SO(n). Indeed, working in such ...

9

... locally **symmetric** **spaces**, based on Helgason’s version of the Fourier transform for this **spaces**, and inspired by the work of Zelditch in the case of G = SL(2, R) ...

40

... spherically **symmetric** manifold relies on the fact that it is possible to decompose the Dirac operator (and analogously its flow) in a sum of ”radial” Dirac operators (see section 3 for details) and so, somehow, ...

37

... This completely describes the topological **spaces** of IRSs in simple higher-rank Lie groups. On the other hand, if G is a group of real rank one then there are always more IRSs than those described in this theorem. ...

28

... ric **spaces**. We consider a spin compact simply connected irreducible **symmetric** space G/K of “type I”, where G is a simple compact and simply-connected Lie group and K is the connected subgroup formed by the ...

26

... the **spaces** SO(p, q) with p < q (recall that the latter **spaces** have a much richer root ...the **spaces** SO(p, q) with p < q, the number of zeroes on the diagonal of D X is ...

16

... of **symmetric** **spaces** like the ...nonlinear **spaces** in such a way that they converge (almost) globally under the same assumptions as linear consensus algorithms, and several solutions were proposed on ...

11

... countable. First the base has to be ordered such that the norm of the rest of the decomposition, i.e., P |j|>N hf, e j i e j , decreases as fast as possible for regular functions. Second, in order to process locations ...

45

... of **symmetric** **spaces**. For example the hy- perbolic **spaces** RH n , CH n , HH n and OH 2 are the only rank one **symmetric** **spaces** of non-compact ...

31

... dimension of secant varieties of Grassmannians, while for our purpose we need the whole description of all the elements in V• V annihilating the given tensor. The idea of extending the apolarity to contexts different ...

25

... The ﬁrst attempt to mix the two requirements was done with **symmetric** Boolean functions. They deserve ﬁrstly attention in cryptography since they guarantee that no input variables has greater or lesser signiﬁcance ...

6