Longest weight vectors and excellent filtrations
type: Item
instance of: scholarly article
title: Longest weight vectors and excellent filtrations
zbMATH Open document ID: 0642.20037
DOI: 10.1007/BF01161991
author: Wilberd van der Kallen
published in: Mathematische Zeitschrift
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174031
review text: Let B be a Borel subgroup in a connected simply connected semisimple algebraic group over an algebraically closed field. In the hope of some day explaining why some features of the representation theory of B are independent of the characteristic, we now develop some homological algebra related with the existence of certain filtrations of B modules. Compare with the ``good filtrations'' of \textit{S. Donkin} [Rational Representations of Algebraic Groups (Lect. Notes Math. 1140, 1985; Zbl 0586.20017)], or the ``excellent filtrations'' of \textit{P. Polo} [Variétés de Schubert et excellentes filtrations. (Preprint 1987)]. See also \textit{A. Joseph} [Ann. Sci. Éc. Norm. Supér., IV. Sér. 18, 389-419 (1985; Zbl 0589.22014)]. In particular, we find a special filtration of the algebra of regular functions on B, viewed as a B bimodule.
reviewed by: Wilberd van der Kallen
Mathematics Subject Classification ID: 20G05
Mathematics Subject Classification ID: 20G10
zbMATH DE Number: 4046020
zbMATH Keywords: Borel subgroup
zbMATH Keywords: connected simply connected semisimple algebraic group
zbMATH Keywords: representation theory
zbMATH Keywords: homological algebra
zbMATH Keywords: filtrations of B modules
zbMATH Keywords: excellent filtrations
zbMATH Keywords: regular functions
MaRDI profile type: Publication
cites work: Schubert varieties and Demazure's character formula
cites work: Q3804882
cites work: On Schur algebras and related algebras. I
cites work: Q3800267
cites work: On the Demazure character formula
cites work: Q3360382
OpenAlex ID: W2051439111
description: scientific article; zbMATH DE number 4046020