Iwahori Matsumoto Presentation for Modules of Iwahori Fixed Functions on Symmetric Spaces

We study the space S(X)I of smooth functions on a symmetric space X=H G invariant to the action of an Iwahori subgroup I, as a module over H(G,I), the Iwahori Hecke algebra of a reductive p-adic group G. We present a description of this module that generalizes the description given to H(G,I) by Iwahori and Matsumoto.