# Epsilon dichotomy for linear models: the Archimedean case

@inproceedings{Suzuki2022EpsilonDF, title={Epsilon dichotomy for linear models: the Archimedean case}, author={Miyu Suzuki and Hiroyoshi Tamori}, year={2022} }

. Let D be a quaternion algebra over R , G = GL n ( D ) and H = GL n ( C ) regarded as a subgroup of G . For a character χ on C × , we say that an irreducible smooth admissible moderate growth representation π of G is χ H -distinguished if Hom H ( π, χ ◦ det H ) 6 = 0. We compute the root number of a χ H -distinguished representation π twisted by the representation induced from χ . This proves an Archimedean analogue of the conjecture by Prasad and Takloo-Bighash (J. Reine Angew. Math., 2011…

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