On Splitting Invariants and Sign Conventions in Endoscopic Transfer

Details On Splitting Invariants and Sign Conventions in Endoscopic Transfer On Splitting Invariants and Sign Conventions in Endoscopic Transfer

2012-01-26

arxiv.org/abs/1201.5658v1

Mathematics

Representation Theory

Scientific paper

The transfer factors for standard endoscopy involve, among other things, the Langlands-Shelstad splitting invariant. This note introduces a twisted version of that splitting invariant. The twisted splitting invariant is then used to define a better twisted factor $\Delta_I$. In addition we correct a sign error in the definition of twisted transfers. There are two ways to correct the sign error. One way yields twisted transfer factors $\Delta'$ that are compatible with the classical Langlands correspondence. The other way yields twisted transfer factors $\Delta_D$ that are compatible with a renormalized version of the Langlands correspondence.

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