Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-10-11
Physics
High Energy Physics
High Energy Physics - Theory
Since a substitution changes f(z) to a multi-valued function we will remove the argument given in the introduction which was n
Scientific paper
The Plancherel formula for the universal covering group of $SL(2, R)$ derived earlier by Pukanszky on which Herb and Wolf build their Plancherel theorem for general semisimple groups is reconsidered. It is shown that a set of unitarily equivalent representations is treated by these authors as distinct. Identification of this equivalence results in a Plancherel measure ($s\mathrm{Re}\tanh\pi(s+\frac{i\tau}{2}), 0\leq\tau<1)$ which is different from the Pukanszky-Herb-Wolf measure ($s\mathrm{Re}\tanh\pi(s+i\tau), 0\leq\tau<1)$.
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