Construction of local A-packets

TL;DR

This paper reformulates the explicit construction of local A-packets for split odd special orthogonal and symplectic groups, providing explicit computation methods, non-vanishing criteria, and formulas for Aubert duals of Arthur type representations.

Contribution

It introduces a new reformulation of Moeglin's construction, enabling explicit computation of A-packets and related representation-theoretic formulas.

Findings

Explicit computation of local A-packets

Non-vanishing criterion for parametrization

Formula for Aubert duals of Arthur type representations

Abstract

In this paper, we reformulate Moeglin's explicit construction of local A-packets of split odd special orthogonal groups and symplectic groups. By this reformulation together with results of the previous paper with Minguez, we can compute the A-packets explicitly. Also, we give a non-vanishing criterion of our parametrization, and an algorithm to compute certain derivatives. Finally, we prove a formula for the Aubert duals of irreducible representations of Arthur type.