Pith. sign in

REVIEW 1 cited by

Endoscopy for Hecke categories, character sheaves and representations

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1904.01176 v3 pith:X6IM7F2M submitted 2019-04-02 math.RT math.AG

classification math.RTmath.AG
keywords characterfixedgroupheckerepresentationssheavescategoryendoscopic
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
abstract

For a split reductive group $G$ over a finite field, we show that the neutral block of its mixed Hecke category with a fixed monodromy under the torus action is monoidally equivalent to the mixed Hecke category of the corresponding endoscopic group $H$ with trivial monodromy. We also extend this equivalence to all blocks. We give two applications. One is a relationship between character sheaves on $G$ with a fixed semisimple parameter and unipotent character sheaves on the endoscopic group $H$, after passing to asymptotic versions. The other is a similar relationship between representations of $G(\mathbb{F}_q)$ with a fixed semisimple parameter and unipotent representations of $H(\mathbb{F}_{q})$.

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

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

  1. Finite Langlands correspondence

    math.NT 2025-08 conditional novelty 6.0 of 10

    Every irreducible representation of a connected reductive group over a finite field is matched with a special Langlands parameter, with the fiber over each parameter given by irreducible representations of a finite co...

Pith tools