Abstract
We could go on producing a list of things that one could do with representations of SL(2, ℝ). And we may be even tempted to draw close analogies between the representation theory of SL(2, ℝ) and SL(n, ℝ) for n ≥ 3. In some senses, there are similarities; but there are also important differences. One of the aims of this chapter is to bring out a fundamental difference between SL(2, ℝ) and SL(n, ℝ) (n ≥ 3). In the process, we also find dramatic differences between harmonic analysis on SL(n, ℝ) and the classical case of ℝ n .
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