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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

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

Uwe Weselmann

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691197890.003.0009

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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