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Kac-Moody groups, hovels and Littelmann paths

Stéphane Gaussent, Guy Rousseau (2008)

Annales de l’institut Fourier

We give the definition of a kind of building ℐ for a symmetrizable Kac-Moody group over a field K endowed with a discrete valuation and with a residue field containing ℂ . 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 K = ℂ ( ( t ) ) , the geodesic segments...

L p - L q estimates for functions of the Laplace-Beltrami operator on noncompact symmetric spaces. III

Michael Cowling, Saverio Giulini, Stefano Meda (2001)

Annales de l’institut Fourier

Let X be a symmetric space of the noncompact type, with Laplace–Beltrami operator - ℒ , and let [ b , ∞ ) be the L 2 ( X ) -spectrum of ℒ . For τ in ℂ such that Re τ ≥ 0 , let 𝒫 τ be the operator on L 2 ( X ) defined formally as exp ( - τ ( ℒ - b ) 1 / 2 ) . In this paper, we obtain L p - L q operator norm estimates for 𝒫 τ for all τ , and show that these are optimal when τ is small and when | arg τ | is bounded below π / 2 .

Les noyaux de Bergman et Szegö pour des domaines strictment pseudo-convexes qui généralisent la boule.

Jean-Jacques Loeb (1992)

Publicacions Matemàtiques

Let G be a complex semi-simple group with a compact maximal group K and an irreducible holomorphic representation ρ on a finite dimensional space V. There exists on V a K-invariant Hermitian scalar product. Let Ω be the intersection of the unit ball of V with the G-orbit of a dominant vector. Ω is a generalization of the unit ball (case obtained for G = SL(n,C) and ρ the natural representation on Cn).We prove that for such manifolds, the Bergman and Szegö kernels as for the ball are rational fractions...

Limit formulas for groups with one conjugacy class of Cartan subgroups

Mladen Božičević (2008)

Annales de l’institut Fourier

Limit formulas for the computation of the canonical measure on a nilpotent coadjoint orbit in terms of the canonical measures on regular semisimple coadjoint orbits arise naturally in the study of invariant eigendistributions on a reductive Lie algebra. In the present paper we consider a particular type of the limit formula for canonical measures which was proposed by Rossmann. The main technical tool in our analysis are the results of Schmid and Vilonen on the equivariant sheaves on the flag variety...

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