THE L_p -DUAL SPACE OF A SEMISIMPLE LIE GROUP
Résumé
Let $G$ be a semisimple Lie group. We describe
the irreducible representations of $G$ by linear isometries
on $L_p$-spaces for $p\in (1,+\infty)$ with $p\neq 2.$
More precisely, we show that, for every such representation $\pi,$
there exists a parabolic subgroup $Q$ of $G$ such that $\pi$ is equivalent to the
natural representation of $G$ on $L_p(G/Q)$
twisted by a unitary character of $Q.$
When $G$ is of real rank one, we give a complete classification of
the possible irreducible representations of $G$ on an $L_p$-space for $p\neq 2,$ up to equivalence.
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