The $L^p$-dual space of a semisimple Lie group
By Bachir Bekka
Appears in collection : 2025 - T1 - WS2 - Tempered representations and K-theory
Given a group $G$ and a real number $p$, it is natural to study representations of G by linear isometries on $L^p$-spaces. Of course, the case where $p$ is equal to 2 corresponds to the familiar and much studied case of unitary representations of $G$. For a semisimple Lie group $G$, we will give a complete classification of all its irreducible $L^p$-representations, for $p\neq2$.
