Duality for nonlinear simply laced groups

TL;DR

This paper develops a duality theory for the representation categories of nonlinear double covers of simply laced real reductive groups, revealing new symmetries in their Harish-Chandra modules.

Contribution

It introduces a uniform character multiplicity duality for Harish-Chandra modules of nonlinear simply laced groups, extending classical duality concepts.

Findings

Establishment of a duality theory for Harish-Chandra modules

Identification of symmetries in character multiplicities

Extension of duality concepts to nonlinear group covers

Abstract

Let G be a nonlinear double cover of the real points of a connected reductive complex algebraic group with simply laced root system. We establish a uniform character multiplicity duality theory for the category of Harish-Chandra modules for G.