The paper constructs L-packets for discrete L-parameters on inner forms of quasi-split disconnected real reductive groups and proves they satisfy endoscopic character identities, establishing the refined local Langlands correspondence.
On the local Langlands conjectures for disconnected groups
3 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We extend the local Langlands conjectures to a certain class of disconnected groups, allowing non-abelian component groups, and recast in this language some aspects of twisted endoscopy. We further introduce normalized twisted transfer factors and a normalized correspondence between an $L$-packet for a disconnected group and the set of representations of the centralizer groups of its Langlands parameter. We prove the first instance of this conjecture, in which the identity component of the (possibly non-abelian) disconnected group is a torus.
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Constructs local Langlands correspondence for essentially unipotent supercuspidal representations of disconnected reductive groups under rigid inner forms, strengthening prior work and proving functoriality.
Germ expansions of Kloosterman integrals are given for p-adic split reductive groups, yielding a conditional proof that Bessel distributions are regular for generic representations assuming bounds on Kloosterman sums for Levi subgroups.
citing papers explorer
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On the refined local Langlands conjecture for discrete $L$-parameters of inner forms of quasi-split disconnected real reductive groups
The paper constructs L-packets for discrete L-parameters on inner forms of quasi-split disconnected real reductive groups and proves they satisfy endoscopic character identities, establishing the refined local Langlands correspondence.
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The local Langlands correspondence of essentially unipotent supercuspidal representations for disconnected reductive groups
Constructs local Langlands correspondence for essentially unipotent supercuspidal representations of disconnected reductive groups under rigid inner forms, strengthening prior work and proving functoriality.
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Bessel Distributions and Kloosterman Sums
Germ expansions of Kloosterman integrals are given for p-adic split reductive groups, yielding a conditional proof that Bessel distributions are regular for generic representations assuming bounds on Kloosterman sums for Levi subgroups.