Generalized Steinberg representations for split reductive groups
نویسندگان
چکیده
منابع مشابه
The Steinberg Variety and Representations of Reductive Groups
We give an overview of some of the main results in geometric representation theory that have been proved by means of the Steinberg variety. Steinberg’s insight was to use such a variety of triples in order to prove a conjectured formula by Grothendieck. The Steinberg variety was later used to give an alternative approach to Springer’s representations and played a central role in the proof of th...
متن کاملRepresentations of Reductive Groups
This course consists of two parts. In the first we will study representations of reductive groups over local non-archimedian fields [ such as Qp and Fq((s))]. In this part I’ll closely follow the notes of the course of J.Bernstein. Moreover I’ll often copy big chanks from these notes. In the second the representations of reductive groups over 2-dimensional local fields [ such as Qp((s))]. In th...
متن کاملOn Extensions of generalized Steinberg Representations
Let F be a local non-archimedean field and let G be the group of F valued points of a connected reductive algebraic group over F. In this paper we compute the Ext-groups of generalized Steinberg representations in the category of smooth G-representations with coefficients in a certain self-injective ring. AMS 2000 Mathematics subject classification: Primary 22E50. Secondary 11F70.
متن کاملMorita’s duality for split reductive groups
In this paper, we extend the work in Morita’s Theory for the Symplectic Groups [7] to split reductive groups. We construct and study the holomorphic discrete series representation and the principal series representation of a split reductive group G over a p-adic field F as well as a duality between certain sub-representations of these two representations.
متن کاملWhittaker Supports for Representations of Reductive Groups
Let F be either R or a finite extension of Qp, and let G be a finite central extension of the group of F -points of a reductive group defined over F . Also let π be a smooth representation of G (Fréchet of moderate growth if F = R). For each nilpotent orbit O we consider a certain Whittaker quotient πO of π. We define the Whittaker support WS(π) to be the set of maximal O among those for which ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Comptes Rendus Mathematique
سال: 2010
ISSN: 1631-073X
DOI: 10.1016/j.crma.2010.01.019