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Local Intertwining Relations and Co-tempered $A$-packets of Classical Groups

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arxiv 2410.13504 v3 pith:RZKUOQOT submitted 2024-10-17 math.NT math.RT

Hiraku Atobe , Wee Teck Gan , Atsushi Ichino , Tasho Kaletha , Alberto Mínguez , Sug Woo Shin This is my paper · ORCID
classification math.NTmath.RT
keywords localintertwiningclassicalgroupsclassificationco-temperedendoscopicinductive
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abstract

The local intertwining relation is an identity that gives precise information about the action of normalized intertwining operators on parabolically induced representations. We prove several instances of the local intertwining relation for quasi-split classical groups and the twisted general linear group, as they are required in the inductive proof of the endoscopic classification for quasi-split classical groups due to Arthur and Mok. In addition, we construct the co-tempered local $A$-packets by Aubert duality and verify their key properties by purely local means, which provide the seed cases needed as an input to the inductive proof. Together with further technical results that we establish, this makes the endoscopic classification conditional only on the validity of the twisted weighted fundamental lemma.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. An algorithm for Aubert-Zelevinsky duality \`a la M{\oe}glin-Waldspurger

    math.RT 2025-09 conditional novelty 7.0 of 10

    For Sp(2n) and SO(2n+1) over a p-adic field, a new recursive combinatorial algorithm computes the Langlands data of the Aubert-Zelevinsky dual of any irreducible representation.

  2. On $A$-parameters containing unitary lowest weight representations of $\mathrm{U}(p, q)$

    math.RT 2025-02 conditional novelty 7.0 of 10

    Every Arthur packet of U(p,q) contains at most one unitary lowest weight representation, with explicit conditions for existence and a formula for the lowest K-type.

  3. The Aubert and Bernstein involutions for disconnected groups

    math.RT 2026-07 accept novelty 6.5 of 10

    Aubert and Bernstein dualities extend to disconnected reductive p-adic groups, with uniqueness, irreducibility preservation, character formulas, and a Steinberg representation for twisted endoscopy.

  4. $p$-adic rigidity for $\mathrm{GSp}_4$

    math.NT 2026-07 conditional novelty 6.5 of 10

    Suitably refined noncuspidal Saito-Kurokawa points for GSp4 are p-adically rigid under Kisin and monodromy hypotheses, so any interpolating family is a point.

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