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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 for a symmetrizable Kac-Moody group over a field K 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 K = ( ( t ) ) , the geodesic segments...

K-finite Whittaker functions are of finite order one

(2013)

Acta Arithmetica

We prove a finite order one type estimate for the Whittaker function attached to a K-finite section of a principle series representation of a real or complex Chevalley group. Effective computations are made using convexity in ℂⁿ, following the original paper of Jacquet. As an application, we give a simplified proof of the known result of the boundedness in vertical strips of certain automorphic L-functions, using a result of Müller.

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