Properties
If G is unimodular, an irreducible unitary representation ρ of G is in the discrete series if and only if one (and hence all) matrix coefficient
with v, w non-zero vectors is square-integrable on G, with respect to Haar measure.
When G is unimodular, the discrete series representation has a formal dimension d, with the property that
for v, w, x, y in the representation. When G is compact this coincides with the dimension when the Haar measure on G is normalized so that G has measure 1.
Read more about this topic: Discrete Series Representation
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