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MR2067697 (2005k:11099) 11F70 (11F55 22E50)
Lansky, Joshua (1AMER); Raghuram, A. (1IA)
Conductors and newforms for U(1, 1). (English summary)
Proc. Indian Acad. Sci. Math. Sci. 114 (2004), no. 4, 319343.
Let F be a nonArchimedean local field whose residue characteristic is odd. The paper under re
view develops a theory of newforms for G = U(1, 1)(F), building on the authors' previous work
on SL2(F) ["Conductors and newforms for SL2", preprint, available at http://www.american.
edu/faculty/lansky/papers/newforms sl2 new.pdf]. The notion of a conductor for an irreducible
admissible representation of G is defined by considering certain filtrations of maximal compact
subgroups of G, and considering the space of fixed vectors under these filtration subgroups. The pa
per investigates the growth of these spaces. The theory is analogous to the results of W. Casselman
[Math. Ann. 201 (1973), 301314; MR0337789 (49 #2558)] and of H. Jacquet, I. I. Piatetski
Shapiro and J. Shalika [Math. Ann. 256 (1981), no. 2, 199214; MR0620708 (83c:22025)]. It is
also proved that the Whittaker functional does not vanish on the newform (the normalised unique
vector in the space of fixed vectors that defines the conductor). This latter result is important in
global applications.
