scholarly journals Counting conjugacy classes in the unipotent radical of parabolic subgroups of GLn(q)

2010 ◽  
Vol 245 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Simon Goodwin ◽  
Gerhard Röhrle
Keyword(s):  
Conjugacy Classes ◽  
Unipotent Radical ◽  
Parabolic Subgroups

scholarly journals Character tables of the maximal parabolic subgroups of the Ree groups 2F4(q2)

2010 ◽  
Vol 13 ◽  
pp. 90-110 ◽  
Author(s):  
Frank Himstedt ◽  
Shih-Chang Huang
Keyword(s):  
Irreducible Character ◽  
Conjugacy Classes ◽  
Unipotent Radical ◽  
Parabolic Subgroups ◽  
Character Tables ◽  
Maximal Parabolic Subgroups

AbstractWe compute the conjugacy classes of elements and the character tables of the maximal parabolic subgroups of the simple Ree groups2F4(q2). For one of the maximal parabolic subgroups, we find an irreducible character of the unipotent radical that does not extend to its inertia subgroup.

scholarly journals Special involutions and bulky parabolic subgroups in finite Coxeter groups

2005 ◽  
Vol 79 (1) ◽  
pp. 141-147 ◽  
Author(s):  
Götz Pfeiffer ◽  
Gerhard Röhrle
Keyword(s):  
Coxeter Group ◽  
Coxeter Groups ◽  
Hyperplane Arrangement ◽  
Conjugacy Classes ◽  
Parabolic Subgroups ◽  
Finite Coxeter Group

AbstractThe conjugacy classes of so-called special involutions parameterize the constituents of the action of a finite Coxeter group on the cohomology of the complement of its complexified hyperplane arrangement. In this note we give a short intrinsic characterisation of special involutions in terms of so-called bulky parabolic subgroups.

Parabolic Subgroups with Abelian Unipotent Radical as a Testing Site for Invariant Theory

1999 ◽  
Vol 51 (3) ◽  
pp. 616-635 ◽  
Author(s):  
Dmitri I. Panyushev
Keyword(s):  
Polynomial Algebra ◽  
Free Module ◽  
Unipotent Radical ◽  
Parabolic Subgroups ◽  
Simple Algebraic Group ◽  
Orbit Closures ◽  
Determinantal Varieties ◽  
Commuting Variety ◽  
Irreducible Components ◽  
Testing Site

AbstractLet L be a simple algebraic group and P a parabolic subgroup with Abelian unipotent radical Pu. Many familiar varieties (determinantal varieties, their symmetric and skew-symmetric analogues) arise as closures of P-orbits in Pu. We give a unified invariant-theoretic treatment of various properties of these orbit closures. We also describe the closures of the conormal bundles of these orbits as the irreducible components of some commuting variety and show that the polynomial algebra k[Pu] is a free module over the algebra of covariants.

Parabolic subgroups with Abelian unipotent radical

1992 ◽  
Vol 110 (1) ◽  
pp. 649-671 ◽  
Author(s):  
Roger Richardson ◽  
Gerhard R�hrle ◽  
Robert Steinberg
Keyword(s):  
Unipotent Radical ◽  
Parabolic Subgroups
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