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Eisenstein Cohomology for GL and the Special Values of Rankin-Selberg L-Functions(AMS-203)$
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Anantharam Raghuram and Günter Harder

Print publication date: 2019

Print ISBN-13: 9780691197890

Published to Princeton Scholarship Online: September 2020

DOI: 10.23943/princeton/9780691197890.001.0001

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The Archimedean Intertwining Operator for GLN

The Archimedean Intertwining Operator for GLN

(p.168) Chapter Nine The Archimedean Intertwining Operator for GLN
Eisenstein Cohomology for GL and the Special Values of Rankin-Selberg L-Functions

Uwe Weselmann

Princeton University Press

This chapter generalizes an identity conjectured by G. Harder and proved by D. Zagier from the case of GL3(ℝ)-representations to the case of general GLN(ℝ)-representations. These are useful in applying the results of Harder and Anantharam Raghuram on quotients of special values of L-functions. To begin, the chapter provides the general setting for this analysis—the group theoretic data and the induced representations. It then discusses the intertwining operators as well as the J-admissible permutations. The chapter goes on to discuss representations and L-functions before turning to the main theorem on Archimedean intertwining operator. Finally, the chapter discusses some applications to cohomology.

Keywords:   Archimedean intertwining operator, L-functions, intertwining operators, J-admissible permutations, cohomology

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