Original scientific paper

https://doi.org/10.21857/m16wjcwv29

Jiang's conjecture and fibers of the Barbasch-Vogan duality

Baiying Liu ; Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA
Chi-Heng Lo ; Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA
Freydoon Shahidi ; Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA

Abstract

The well-known Shahidi's conjecture says that tempered L-packets have generic members. As a natural generalization of Shahidi's conjecture to non-tempered local Arthur packets, Jiang's conjecture characterizes the relation between the structure of local Arthur parameters and the upper bound of wavefront sets of representations in local Arthur packets. One of the main ingredients in Jiang's conjecture is the Barbasch-Vogan duality. In this paper, first we briefly survey the recent progress on Jiang's conjecture, then towards the general case of Jiang's conjecture, we explicitly describe the fibers of the Barbasch-Vogan duality for classical groups.

Keywords

Local Arthur packets; Local Arthur parameters; Shahidi's conjecture; enhanced Shahidi's conjecture; Jiang's conjecture

Hrčak ID:

313627

URI

https://hrcak.srce.hr/313627

Publication date:

24.1.2024.

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