Bernstein-Zelevinsky duality for locally analytic principal series representations

TL;DR

This paper explores Bernstein-Zelevinsky duality for locally analytic principal series representations of p-adic Lie groups, connecting dual complexes with Grothendieck-Serre duality on eigenvarieties.

Contribution

It introduces a duality framework for integral weight principal series and relates it to dualities in geometric and representation-theoretic contexts.

Findings

Dual complexes compute Bernstein-Zelevinsky duals

Establishes Grothendieck-Serre duality on eigenvarieties

Links duality in representation theory with geometric dualities

Abstract

We consider certain dual of the Kohlhaase-Schraen resolutions for locally analytic principal series representations of $p$-adic Lie groups in the case of integral weights. The dual complexes calculate the expected Bernstein-Zelevinsky dual of the locally analytic representations and lead to the Grothendieck-Serre duality of coherent sheaves on patched eigenvarieties.