The
line model for GL(2,R)

•Here N is one
dimensional, isomorphic to R.

•NÅ G ' Z

•So t 2 C-1(ZnR) is a distribution on the circle, hence has a Fourier expansion

t(x) = ån2 Z cn e(nx)

with e(x) = e2p i x and
some coefficients cn.

•The G-action in the line model is

•Therefore:

For simplicity, set
l = (n,-n), d = (0,0), and G = SL(2,Z)