Abstract
In this chapter we give an explicit formula for the Archimedean transfer factor of Langlands and Shelstad [60]. Since it makes no essential difference, we do this for type I elliptic tori over an arbitrary local field of characteristic zero (elliptic tori of type II do not occur over Archimedean local fields). The Archimedean transfer factor is important for the global property of the transfer factors (product formula) necessary for the stabilization of the trace formula. The Archimedean transfer factor, on the other hand, determines the endoscopic lift at the Archimedean place by the results obtained by Shelstad [90]. For us this is crucial since it implicitly determines the relevant sign ε that appears in Corollary 4.1 to be ε = ?1 (via the theory of Whittaker models in Sect. 4.10 and some global multiplicity arguments).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Weissauer, R. (2009). The Langlands-Shelstad transfer factor. In: Endoscopy for GSp(4) and the Cohomology of Siegel Modular Threefolds. Lecture Notes in Mathematics(), vol 1968. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89306-6_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-89306-6_8
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-89305-9
Online ISBN: 978-3-540-89306-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)