Year: 2026
Type: article
Abstract: Let G G be a real classical group (including the real metaplectic group). We consider a nilpotent adjoint orbit O ˇ \check {\mathcal O} of G ˇ \check G , the Langlands dual of G G (or the metaplectic Langlands dual of G G when G G is a real metaplectic group). We classify all special unipotent representations of G G attached to O ˇ \check {\mathcal O} , in the sense of Arthur and Adams-Barbasch-Vogan. When O ˇ \check {\mathcal O} has good parity in the sense of Mœglin, we construct all such representations of G G via the method of theta lifting. As a consequence of the construction and the classification, we conclude that all special unipotent representations of G G are unitarizable, as predicted by the Arthur-ABV conjecture. We also determine the precise structure of the associated cycles of special unipotent representations of G G . The paper is the second in a series of two papers on the classification of special unipotent representations of real classical groups.
DOI: 10.1090/jams/1082
Authors: Dan Barbasch, Jia-Jun Ma, Binyong Sun, Chen-Bo Zhu
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1227676057, G1416364959, G1850847857, G1967736879, G2154040637, G2694685828, G3631825126, G3715398399, Special Projects: Workshop to Establish a Research Agenda in Learning Science and Technology, G3807221932, G3985534342, G4021019611, G4188287416, G4197854740, G4561029024, G4614503521, G5128722646, G5169776950, G5498417828, G5546939681, G5574584734, G5933164787, G6011569594, G6369229954, G7204905774, G804221678, G8133029712, G8343080523, Unipotent Representations and Associated Cycles, G8890111433, G925045915
OpenAlex ID: W4293050286