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Construction of local A-packets

Hiraku Atobe EMAIL logo

Abstract

In the present paper, we reformulate Mœglin’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 Mínguez, 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.

Award Identifier / Grant number: 19K14494

Funding statement: The author was supported by JSPS KAKENHI Grant Number 19K14494.

Acknowledgements

We would like to thank Bin Xu for answering our questions and for suggesting his result for the proof of Theorem 6.2. We are grateful to Alberto Mínguez for useful discussions. Thanks are also due to the referee for the careful readings and the helpful comments. A Sage code for computing examples of several objects in this paper is now available at https://github.com/atobe31/Local-A-packets. We are grateful to Alexander Hazeltine, Baiying Liu and Chi-Heng Lo for pointing out many bugs.

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Received: 2021-04-19
Revised: 2022-04-06
Published Online: 2022-06-29
Published in Print: 2022-09-01

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