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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.

Contact and conformal maps on Iwasawa N groups

Michael Cowling, Filippo De Mari, Adam Korányi, Hans Martin Reimann (2002)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The action of the conformal group O ⁢ 1 , n + 1 on R n ∪ ∞ may be characterized in differential geometric terms, even locally: a theorem of Liouville states that a C 4 map between domains U and V in R n whose differential is a (variable) multiple of a (variable) isometry at each point of U is the restriction to U of a transformation x → g ⋅ x , for some g in O ⁢ 1 , n + 1 . In this paper, we consider the problem of characterizing the action of a more general semisimple Lie group G on the space G / P , where P is a parabolic subgroup. We solve...

Control systems on semi-simple Lie groups and their homogeneous spaces

Velimir Jurdjevic, Ivan Kupka (1981)

Annales de l'institut Fourier

In the present paper, we consider the class of control systems which are induced by the action of a semi-simple Lie group on a manifold, and we give a sufficient condition which insures that such a system can be steered from any initial state to any final state by an admissible control. The class of systems considered contains, in particular, essentially all the bilinear systems. Our condition is semi-algebraic but unlike the celebrated Kalman criterion for linear systems, it is not necessary. In...

Controllability of right invariant systems on semi-simple Lie groups

R. El Assoudi, J. Gauthier, I. Kupka (1995)

Banach Center Publications

We deal with controllability of right invariant control systems on semi-simple Lie groups. We recall the history of the problem and the successive results. We state the final complete result, with a sketch of proof.

Currently displaying 81 – 100 of 384