The L_p-dual space of a semisimple Lie group

2024/05/21 by Bekka, Bachir
#22E46 #37A40 #47L10 #Dynamical Systems (math.DS) #FOS: Mathematics #Operator Algebras (math.OA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2405.12919

Abstract

Let G be a semisimple Lie group. We describe the irreducible representations of G by linear isometries on L_p-spaces for p∈ (1,+∞) with p≠ 2. More precisely, we show that, for every such representation π, there exists a parabolic subgroup Q of G such that π 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≠ 2, up to equivalence.

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