2022/11/04 by Jena, Akash
#22E50 #FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2211.02761
Let G be a p-adic Lie group with reductive Lie algebra \mathfrakg. Denote by D(G) the locally analytic distribution algebra of G. Orlik-Strauch and Agrawal-Strauch have studied certain exact functors defined on various categories of \mathfrakg-representations with image in the category of locally analytic G-representations or D(G)-modules. In this paper we prove that for suitably defined categories of D(G)-modules, this functor gives rise to injective homomorphisms at the level of Grothendieck groups. We also explain how this functor interacts with translation functors at the level of Grothendieck groups.