Vogan Duality for ~Spin(p,q)

TL;DR

This paper explores a symmetry in genuine parameters for even rank nonlinear Spin groups, establishing a duality in Hecke modules and character multiplicities at specific infinitesimal characters.

Contribution

It introduces a novel Vogan duality for Spin(p,q) groups, linking genuine parameters and Hecke modules at half-integral infinitesimal characters.

Findings

Identifies a symmetry in genuine parameters for Spin groups.

Establishes a duality of generalized Hecke modules.

Demonstrates character multiplicity duality.

Abstract

The main purpose of this paper is to describe a symmetry in the set genuine parameters for even rank nonlinear Spin groups in type B at certain half-integral infinitesimal characters. This symmetry is used to establish a duality of the corresponding generalized Hecke modules and ultimately results in a character multiplicity duality of the induced genuine characters.