Parabolic subgroups of algebraic groups and induction

1986 ◽  
Vol 62 (347) ◽  
pp. 0-0
Author(s):  
David C. Vella
Keyword(s):  
Algebraic Groups ◽  
Parabolic Subgroups

scholarly journals Overgroups of regular unipotent elements in simple algebraic groups

2021 ◽  
Vol 8 (25) ◽  
pp. 788-822
Author(s):  
Gunter Malle ◽  
Donna Testerman
Keyword(s):  
Algebraic Groups ◽  
Parabolic Subgroups ◽  
Connected Component ◽  
Unipotent Element

We investigate positive-dimensional closed reductive subgroups of almost simple algebraic groups containing a regular unipotent element. Our main result states that such subgroups do not lie inside proper parabolic subgroups unless possibly when their connected component is a torus. This extends the earlier result of Testerman and Zalesski treating connected reductive subgroups.

scholarly journals Loewy series of parabolically induced -Verma modules

2014 ◽  
Vol 14 (1) ◽  
pp. 185-220 ◽  
Author(s):  
Abe Noriyuki ◽  
Kaneda Masaharu
Keyword(s):  
Algebraic Group ◽  
Positive Characteristic ◽  
Algebraic Groups ◽  
Minimal Length ◽  
Closed Field ◽  
Verma Modules ◽  
Parabolic Subgroups ◽  
Reductive Algebraic Group ◽  
Frobenius Kernel ◽  
Field Of Positive Characteristic

AbstractWe show that the modules for the Frobenius kernel of a reductive algebraic group over an algebraically closed field of positive characteristic $p$ induced from the $p$-regular blocks of its parabolic subgroups can be $\mathbb{Z}$-graded. In particular, we obtain that the modules induced from the simple modules of $p$-regular highest weights are rigid and determine their Loewy series, assuming the Lusztig conjecture on the irreducible characters for the reductive algebraic groups, which is now a theorem for large $p$. We say that a module is rigid if and only if it admits a unique filtration of minimal length with each subquotient semisimple, in which case the filtration is called the Loewy series.

A Semigroup Approach to Linear Algebraic Groups III. Buildings

1986 ◽  
Vol 38 (3) ◽  
pp. 751-768 ◽  
Author(s):  
Mohan S. Putcha
Keyword(s):  
Algebraic Groups ◽  
Usual Sense ◽  
Closed Field ◽  
Parabolic Subgroups ◽  
Algebraically Closed Field ◽  
Linear Algebraic Groups ◽  
Semigroup Approach ◽  
Image Position

Introduction. Let K be an algebraically closed field, G = SL(3, K) the group of 3 × 3 matrices over K of determinant 1. Let denote the monoid of all 3 × 3 matrices over K. If e is an idempotent in , thenare opposite parabolic subgroups of G in the usual sense [1], [28]. However the mapdoes not exhaust all pairs of opposite parabolic subgroups of G. Now consider the representation ϕ:G → SL(6, K) given by

scholarly journals On the Structure of Parabolic Subgroups in Algebraic Groups

1993 ◽  
Vol 157 (1) ◽  
pp. 80-115 ◽  
Author(s):  
G.E. Rohrle
Keyword(s):  
Algebraic Groups ◽  
Parabolic Subgroups
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