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Theta series for the exceptional groups are relevant to the representation theory of non-compact groups, quantum mechanical models/dynamical systems with hidden symmetries and possibly even M theory--the purported stringy Theory Of Everything! Theta series are objects whose group invariances involve an action via Fourier transform. The problem of constructing them for exceptional groups is a topic of current research, but fortunately, the main ideas involved can be explained in the case of a much simpler group, Sl(2)--2x2 matrices with unit determinant. The paper http://xxx.lanl.gov/abs/hep-th/0107222 may be good backround reading!