Abstract
1. Let K be a non-archimedean local field with the residue field consisting of q. elements. According to “Langlands philosophy” irreducible complex representations of a reductive K-group G, should roughly speaking correspond to homomorphisms of the Weil-Deligne group into the socalled L-group. Let Zc G, be the Iwahori subgroup. The category of admissible GKmodules, generated by Z-fixed vectors, is known to be equivalent to the category of finite-dimensional representations of the Hecke algebra H(Z\G,/Z). “Langlands philosophy” suggests via that equivalence the following classification of irreducible Hecke algebra modules (stated in purely complex terms and not involving any local held):
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