  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.
