An inverse Satake isomorphism in characteristic

作者：Ollivier Rachel^*

来源：Selecta Mathematica, New Series, 2015, 21(3): 727-761.

DOI：10.1007/s00029-014-0157-7

Let be a local field with finite residue field of characteristic and an algebraic closure of the residue field. Let be the group of -points of a -split connected reductive group. In the apartment corresponding to a maximal split torus , we choose a hyperspecial vertex and denote by the corresponding maximal compact subgroup of . Given an irreducible smooth -representation of , we construct an isomorphism from the affine semigroup -algebra of the dominant cocharacters of onto the spherical -algebra . In the case when the derived subgroup of is simply connected, we prove furthermore that our isomorphism is the inverse to the mod Satake isomorphism constructed by Herzig (Compos Math 147(1):263-283, 2011).

• 出版日期2015-7