Another
model for Principal Series

•Principal series are
modeled on sections of line bundles over the flag varieties G/B.

•G/B has a dense, open “big
Bruhat cell” N = {unit upper triangular matrices}.

•Functions in Vl,d1 are of course
determined by their restriction to this dense cell; distributions, however, are not.

•However, automorphic distributions have a large invariance group, so in fact are determined by their restriction to N.

•__Upshot__: instead of studying
automorphic forms on a large dimensional space G, we may study distributions on a space N which
has < half the dimension. View t 2 C-1(NÅ GnN).

•Another positive: no special functions are needed.

•A negative: requires dealing with distributions instead of functions, and
hence some analytic overhead.