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Constant term in Harish-Chandra’s limit formula

Mladen Božičević (2008)

Annales mathématiques Blaise Pascal

Let G 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 -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.

Construction techniques for some thin sets in duals of compact abelian groups

D. J. Hajela (1986)

Annales de l'institut Fourier

Various techniques are presented for constructing Λ (p) sets which are not Λ ( p + ϵ ) for all ϵ > 0 . The main result is that there is a Λ (4) set in the dual of any compact abelian group which is not Λ ( 4 + ϵ ) for all ϵ > 0 . Along the way to proving this, new constructions are given in dual groups in which constructions were already known of Λ (p) not Λ ( p + ϵ ) sets, for certain values of p . The main new constructions in specific dual groups are:– there is a Λ (2k) set which is not Λ ( 2 k + ϵ ) in Z ( 2 ) Z ( 2 ) for all 2 k , k N and ϵ > 0 , and in Z ( p ) Z ( p ) ( p a prime,...

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...

Continued fractions on the Heisenberg group

Anton Lukyanenko, Joseph Vandehey (2015)

Acta Arithmetica

We provide a generalization of continued fractions to the Heisenberg group. We prove an explicit estimate on the rate of convergence of the infinite continued fraction and several surprising analogs of classical formulas about continued fractions.

Continuous actions of pseudocompact groups and axioms of topological group

Alexander V. Korovin (1992)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we show that it is possible to extend the Ellis theorem, establishing the relations between axioms of a topological group on a new class 𝒩 of spaces containing all countably compact spaces in the case of Abelian group structure. We extend statements of the Ellis theorem concerning separate and joint continuity of group inverse on the class of spaces 𝒩 that gives some new examples and statements for the C p -theory and theory of topologically homogeneous spaces.

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