Iwahori Matsumoto presentation for modules of Iwahori fixed functions on symmetric spaces · arXivDesk2406.16070Jun 23, 2024Changed notations of right actions; Added Definitions 2.37, 3.5, Propositions 2.38, 3.6, and Examples 6.7, 7.3;
Iwahori Matsumoto presentation for modules of Iwahori fixed functions on symmetric spaces
Guy Shtotland
Abstract
We study the space S(X)I of smooth functions on a symmetric space X=G/H invariant to the action of an Iwahori subgroup I, as a module over H(G,I)
, the Iwahori Hecke algebra of a p-adic group
. We present a description of this module that generalizes the description given to
H(G,I) by Iwahori and Matsumoto.