Displaying similar documents to “Proof of the Knop conjecture”

Kac-Moody groups, hovels and Littelmann paths

Stéphane Gaussent, Guy Rousseau (2008)

Annales de l’institut Fourier

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We give the definition of a kind of building for a symmetrizable Kac-Moody group over a field endowed with a discrete valuation and with a residue field containing . Due to the lack of some important property of buildings, we call it a hovel. Nevertheless, some good ones remain, for example, the existence of retractions with center a sector-germ. This enables us to generalize many results proved in the semisimple case by S. Gaussent and P. Littelmann. In particular, if , the geodesic...

Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks

Masafumi Yoshino, Todor Gramchev (2008)

Annales de l’institut Fourier

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We study the simultaneous linearizability of –actions (and the corresponding -dimensional Lie algebras) defined by commuting singular vector fields in fixing the origin with nontrivial Jordan blocks in the linear parts. We prove the analytic convergence of the formal linearizing transformations under a certain invariant geometric condition for the spectrum of vector fields generating a Lie algebra. If the condition fails and if we consider the situation where small denominators...

Effective equidistribution of S-integral points on symmetric varieties

Yves Benoist, Hee Oh (2012)

Annales de l’institut Fourier

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Let be a global field of characteristic not 2. Let be a symmetric variety defined over and a finite set of places of . We obtain counting and equidistribution results for the S-integral points of . Our results are effective when is a number field.