TY - JOUR
T1 - ON ARTHUR’S UNITARITY CONJECTURE FOR SPLIT REAL GROUPS
AU - Hundley, Joseph
AU - Miller, Stephen D.
N1 - Funding Information:
Manuscript received September 5, 2019. Research of the first author supported by NSA grants H98230-15-1-0234 and H98230-16-1-0125; research of the second author supported by NSF grants DMS-1801417 and CNS-1815562. American Journal of Mathematics 144 (2022), 1561–1600. © 2022 by Johns Hopkins University Press.
Publisher Copyright:
© 2022 by Johns Hopkins University Press.
PY - 2022/12
Y1 - 2022/12
N2 - Arthur’s conjectures predict the existence of some very interesting unitary representations occurring in spaces of automorphic forms. We prove the unitarity of the “Langlands element” (i.e., the representation specified by Arthur) of all unipotent Arthur packets for split real exceptional groups. The proof uses Eisenstein series, Langlands’ constant term formula and square integrability crite-rion, analytic properties of intertwining operators, and some mild arithmetic input from the theory of Dirichlet L-functions, to reduce to a more combinatorial problem about intertwining operators.
AB - Arthur’s conjectures predict the existence of some very interesting unitary representations occurring in spaces of automorphic forms. We prove the unitarity of the “Langlands element” (i.e., the representation specified by Arthur) of all unipotent Arthur packets for split real exceptional groups. The proof uses Eisenstein series, Langlands’ constant term formula and square integrability crite-rion, analytic properties of intertwining operators, and some mild arithmetic input from the theory of Dirichlet L-functions, to reduce to a more combinatorial problem about intertwining operators.
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U2 - 10.1353/ajm.2022.0038
DO - 10.1353/ajm.2022.0038
M3 - Article
AN - SCOPUS:85143523974
SN - 0002-9327
VL - 144
SP - 1561
EP - 1600
JO - American Journal of Mathematics
JF - American Journal of Mathematics
IS - 6
ER -