Abstract
Let G be a split reductive group over a p-adic field F. Let B be a Borel subgroup and U the maximal unipotent subgroup of B. Let \(\psi \) be a Whittaker character of U. Let I be an Iwahori subgroup of G. We describe the Iwahori–Hecke algebra action on the Gelfand–Graev representation \((\mathrm {ind}_{U}^{G}\psi )^I\) by an explicit Hecke algebra module.
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