All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 35 Next

Displaying 681 – 700 of 3839

Showing per page

Conformally invariant trilinear forms on the sphere

Jean-Louis Clerc, Bent Ørsted (2011)

Annales de l’institut Fourier

To each complex number λ is associated a representation π λ of the conformal group S O 0 ( 1 , n ) on 𝒞 ∞ ( S n - 1 ) (spherical principal series). For three values λ 1 , λ 2 , λ 3 , we construct a trilinear form on 𝒞 ∞ ( S n - 1 ) × 𝒞 ∞ ( S n - 1 ) × 𝒞 ∞ ( S n - 1 ) , which is invariant by π λ 1 ⊗ π λ 2 ⊗ π λ 3 . The trilinear form, first defined for ( λ 1 , λ 2 , λ 3 ) in an open set of ℂ 3 is extended meromorphically, with simple poles located in an explicit family of hyperplanes. For generic values of the parameters, we prove uniqueness of trilinear invariant forms.

Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane

Yuri L. Sachkov (2010)

ESAIM: Control, Optimisation and Calculus of Variations

The left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is studied. Local and global optimality of extremal trajectories is characterized. Lower and upper bounds on the first conjugate time are proved. The cut time is shown to be equal to the first Maxwell time corresponding to the group of discrete symmetries of the exponential mapping. Optimal synthesis on an open dense subset of the state space is described.

Connected abelian complex Lie groups and number fields

Daniel Vallières (2012)

Journal de Théorie des Nombres de Bordeaux

In this note we explain a way to associate to any number field some connected complex abelian Lie groups. Further, we study the case of non-totally real cubic number fields, and we see that they are intimately related with the Cousin groups (toroidal groups) of complex dimension 2 and rank 3 .

Connected LCA groups are sequentially connected

Shou Lin, Mihail G. Tkachenko (2013)

Commentationes Mathematicae Universitatis Carolinae

We prove that every connected locally compact Abelian topological group is sequentially connected, i.e., it cannot be the union of two proper disjoint sequentially closed subsets. This fact is then applied to the study of extensions of topological groups. We show, in particular, that if H is a connected locally compact Abelian subgroup of a Hausdorff topological group G and the quotient space G / H is sequentially connected, then so is G .

Constant term in Harish-Chandra’s limit formula

Mladen Božičević (2008)

Annales mathématiques Blaise Pascal

Let G ℝ be a real form of a complex semisimple Lie group G . Recall that Rossmann defined a Weyl group action on Lagrangian cycles supported on the conormal bundle of the flag variety of G . We compute the signed average of the Weyl group action on the characteristic cycle of the standard sheaf associated to an open G ℝ -orbit on the flag variety. This result is applied to find the value of the constant term in Harish-Chandra’s limit formula for the delta function at zero.

Currently displaying 681 – 700 of 3839