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A lemma on highly ramified $$\epsilon$$-factors. (English) Zbl 0541.12010
A standard property of the $$\epsilon$$-factor attached to a representation of the Weil group W of a local field F is the following: given $$\sigma_ 1$$ and $$\sigma_ 2$$ with the same determinant, let $$\sigma_ 1\otimes \chi$$ and $$\sigma_ 2\otimes \chi$$ be the tensor products with a character $$\chi$$ of $$F^{\times}$$ (identified with a character of W); then, if the conductor of $$\chi$$ is sufficiently big, the $$\epsilon$$- factors for $$\sigma_ 1\otimes \chi$$ and $$\sigma_ 2\otimes \chi$$ coincide. Similarly, to every pair of irreducible representations of general linear groups, one can attach an $$\epsilon$$-factor: it is established that it has the corresponding property.

##### MSC:
 11S37 Langlands-Weil conjectures, nonabelian class field theory 22E50 Representations of Lie and linear algebraic groups over local fields 11F70 Representation-theoretic methods; automorphic representations over local and global fields
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##### References:
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