On Satake Parameters for Representations with Parahoric Fixed Vectors
نویسنده
چکیده
This article, a continuation of [HRo], constructs the Satake parameter for any irreducible smooth J-spherical representation of a p-adic group, where J is any parahoric subgroup. This parametrizes such representations when J is a special maximal parahoric subgroup. The main novelty is for groups which are not quasi-split, and the construction should play a role in formulating a geometric Satake isomorphism for such groups over local function fields.
منابع مشابه
Iwahori–spherical representations of GSp(4) and Siegel modular forms of degree 2 with square-free level
A theory of local old– and newforms for representations of GSp(4) over a p–adic field with Iwahori– invariant vectors is developed. The results are applied to Siegel modular forms of degree 2 with square-free level with respect to various congruence subgroups. Introduction For representations of GL(2) over a p–adic field F there is a well-known theory of local newforms due to Casselman, see [Ca...
متن کاملThe Satake Isomorphism for Special Maximal Parahoric Hecke Algebras
Let G denote a connected reductive group over a nonarchimedean local field F . Let K denote a special maximal parahoric subgroup of G(F ). We establish a Satake isomorphism for the Hecke algebra HK of K-bi-invariant compactly supported functions on G(F ). The key ingredient is a Cartan decomposition describing the double coset space K\G(F )/K. We also describe how our results relate to the trea...
متن کاملSpherical representations and the Satake isomorphism
Last updated: December 10, 2013. Topics: Motivation for the study of spherical representations; Satake isomorphism stated for the general case of a connected reductive group (taking Bruhat-Tits theory as a black box); interpretation (spherical principal series, Satake parameter, representations of dual reductive group); Satake made more explicit for the split case (key calculation); idea of pro...
متن کاملThe Geometry of Fixed Point Varieties on Affine Flag Manifolds
Let G be a semisimple, simply connected, algebraic group over an algebraically closed field k with Lie algebra g. We study the spaces of parahoric subalgebras of a given type containing a fixed nil-elliptic element of g⊗k((π)), i.e. fixed point varieties on affine flag manifolds. We define a natural class of k-actions on affine flag manifolds, generalizing actions introduced by Lusztig and Smel...
متن کاملRepresentations of Double Coset Lie Hypergroups
We study the double cosets of a Lie group by a compact Lie subgroup. We show that a Weil formula holds for double coset Lie hypergroups and show that certain representations of the Lie group lift to representations of the double coset Lie hypergroup. We characterize smooth (analytic) vectors of these lifted representations.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014