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

Key Points

• This study aims to describe the space of smooth functions invariant under the action of an Iwahori subgroup on symmetric spaces.
• Exploration of the space of smooth functions on the symmetric space $X=H\backslash G$.
• Analysis of the module structure over the Iwahori Hecke algebra $\mathcal{H}(G,I)$.
• Generalization of existing descriptions provided by Iwahori and Matsumoto.
• Presentation of a new generalized description of the module of smooth functions.
• Identification of properties linking the smooth functions and the Iwahori Hecke algebra.