The Plancherel Formula for the Universal Covering Group of SL2,R Revisited - High Energy Physics - TheoryReport as inadecuate




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Abstract: The Plancherel formula for the universal covering group of $SL2, R$ derivedearlier by Pukanszky on which Herb and Wolf build their Plancherel theorem forgeneral semisimple groups is reconsidered. It is shown that a set of unitarilyequivalent representations is treated by these authors as distinct.Identification of this equivalence results in a Plancherel measure$s\mathrm{Re}\tanh\pis+\frac{i\tau}{2}, 0\leq\tau<1$ which is differentfrom the Pukanszky-Herb-Wolf measure $s\mathrm{Re}\tanh\pis+i\tau,0\leq\tau<1$.



Author: Debabrata Basu

Source: https://arxiv.org/







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