On Splitting Invariants and Sign Conventions in Endoscopic Transfer

Abstract

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 ${\Delta }^{\prime }$ 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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