L-packets over strong real forms

Arancibia Robert, N.; Mezo, P.

doi:10.1090/ert/667

L-packets over strong real forms
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by N. Arancibia Robert and P. Mezo

Represent. Theory 28 (2024), 20-48

DOI: https://doi.org/10.1090/ert/667

Published electronically: January 5, 2024

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Abstract:

Langlands [On the classification of irreducible representations of real algebraic groups, Math. Surveys Monogr., vol. 31, Amer. Math. Soc., Providence, RI, 1989, pp. 101–170] defined $L$-packets for real reductive groups. In order to refine the local Langlands correspondence, Adams-Barbasch-Vogan [The Langlands classification and irreducible characters for real reductive groups, Progress in Mathematics, vol. 104, Birkhäuser Boston, Inc., Boston, MA, 1992] combined L-packets over all real forms belonging to an inner class. In the tempered setting, using different methods, Kaletha [Ann. of Math. (2) 184 (2016), pp. 559–632] also defines such combined L-packets with a refinement to the local Langlands correspondence. We prove that the tempered L-packets of Adams-Barbasch-Vogan and Kaletha are the same and are parameterized identically.

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