Establishes reciprocity of wavefront sets and proves the Wavefront Set Conjecture for generic L-parameter representations of classical groups, determining the microlocal structure of characters via arithmetic L-data.
Endoscopic Classification of Representations: Inner Forms of Unitary Groups
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abstract
We classify the automorphic representations (over number fields) and the irreducible admissible representations (over local fields) of unitary groups which are not quasi-split, under the assumption that the same is known for quasi-split unitary groups. The classification of automorphic representations is given in terms of automorphic representations of general linear groups. The classification of irreducible admissible representations is given in terms of Langlands parameters.
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2026 1verdicts
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Arithmetic Wavefront Set and Microlocal Structure of Harish-Chandra Character
Establishes reciprocity of wavefront sets and proves the Wavefront Set Conjecture for generic L-parameter representations of classical groups, determining the microlocal structure of characters via arithmetic L-data.