On calibrated representations and the Plancherel Theorem for affine Hecke algebras

James Parkinson

Published 2011-10-27, updated 2014-05-26Version 2

This paper has two main purposes. Firstly we generalise Ram's explicit 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 including a construction of all representations involved (following work of Opdam).