Summary: Zentralblatt MATH Database 1931 2009
c 2009 European Mathematical Society, FIZ Karlsruhe & Springer-Verlag
Anandavardhanan, U.K.; Kable, Anthony C.; Tandon, R.
Distinguished representations and poles of twisted tensor L-functions. (Eng-
Proc. Am. Math. Soc. 132, No. 10, 2875-2883 (2004). ISSN 0002-9939; ISSN 1088-6826
Let E/F be a quadratic extension of p-adic fields. Let be a representation of GL(n, E)
normalizedly parabolically induced from a square-integrable irreducible representation.
Let Pn(F) be the group of matrices in GL(n, F) with bottom row (0, . . . , 0, 1). This
work shows that there is a unique Pn(F)-invariant complex-valued nonzero linear form
on , up to a scalar. It is then deduced that if is distinguished by GL(n, F), then the
twisted tensor L-function of , introduced in the reviewer's "Twisted tensors and Euler
products", [Bull. Soc. Math. Fr. 116, 295313 (1988; Zbl 0674.10026)], has a pole at
s = 0. It follows that if is discrete series, at most one of and E/F is distinguished,
in agreement with the conjecture introduced by the reviewer in "On distinguished rep-
resentations", [J. Reine Angew. Math. 418, 139172 (1991; Zbl 0725.11026)], on the