An arithmetic property of intertwining operators for p-adic groups
Abstract
If one proposes to use the theory of Eisenstein cohomology to prove algebraicity results for the special values of automorphic L-functions as in my work with Harder for Rankin-Selberg L-functions, or its generalizations as in my work with Bhagwat for L-functions for orthogonal groups and independently with Krishnamurthy on Asai L-functions, then in a key step, one needs to prove that the normalised standard intertwining operator between induced representations for p-adic groups has a certain arithmetic property. The principal aim of this article is to address this particular local problem in the generality of the Langlands-Shahidi machinery. The main result of this article is invoked in some of the works mentioned above, and I expect that it will be useful in future investigations on the arithmetic properties of automorphic L-functions.
Cite
@article{arxiv.2106.00960,
title = {An arithmetic property of intertwining operators for p-adic groups},
author = {A. Raghuram},
journal= {arXiv preprint arXiv:2106.00960},
year = {2021}
}