On calibrated representations and the Plancherel Theorem for affine Hecke algebras

This paper has two main purposes. Firstly, we generalise Ram’s combinatorial construction of calibrated representations of the affine Hecke algebra to the multi-parameter case (including the non-reduced BC _n case). We then derive the Plancherel formulae for all rank 1 and rank 2 affine Hecke algebras, using our calibrated representations to construct all representations involved.