Rad HAZU, Matematičke znanosti, Vol. 28 (2024), 107-129.

JIANG’S CONJECTURE AND FIBERS OF THE BARBASCH-VOGAN DUALITY

Baiying Liu, Chi-Heng Lo and Freydoon Shahidi

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.

2020 Mathematics Subject Classification.   11F70, 22E50, 11F85.

Key words and phrases.   Local Arthur packets, Local Arthur parameters, Shahidi's conjecture, enhanced Shahidi's conjecture, Jiang's conjecture.

DOI: https://doi.org/10.21857/m16wjcwv29

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